delivered the opinion of the court:
Following a bench trial in the circuit court of Cook County, the defendant, Jimmie Tye, was convicted of the murder of his three-year-old daughter, Jasmin James. *7The State requested a hearing to determine whether the defendant should be sentenced to death for the offense. The defendant waived a jury for purposes of the sentencing hearing. The trial judge determined that the defendant was eligible for the death penalty and that there were no mitigating circumstances sufficient to preclude imposition of that sentence. The judge accordingly sentenced the defendant to death. The defendant’s execution was stayed pending direct appeal to this court. (Ill. Const. 1970, art. VI, §4(b); 107 Ill. 2d Rules 603, 609(a).) In the present appeal, the defendant raises a number of challenges to the proceedings below. We affirm the defendant’s conviction and sentence.
The evidence presented at trial was, in the main, undisputed; the principal disagreement concerned the defendant’s mental state at the time of the occurrence. The State introduced into evidence the defendant’s confession, in which he acknowledged whipping his daughter with a belt and electrical cord on the night of her death. The State also presented autoptic evidence, which detailed the severity of the beating the child suffered. The defendant maintained that he acted only recklessly in beating Jasmin, and that involuntary manslaughter was the most serious offense for which he could be convicted.
At the time of the occurrence, the defendant and Pamela James lived in Chicago with their two children, Jasmin, who was three years old, and Alicia, who was five months old. On October 24, 1984, Pamela left the apartment around 6 p.m., for an appointment with her hairdresser. The defendant was to look after the two children in Pamela’s absence. The defendant fed the children their dinner. Later, that evening, around 10 o’clock, the defendant told Jasmin to go to bed. When Jasmin refused to do so, the defendant struck her several times with his belt. Jasmin still refused to go to bed, and the defendant struck her again with the belt.
*8The defendant then got a 14-foot extension cord from another room. The defendant ordered Jasmin to lower her pants, folded the cord, and beat her with it. The defendant then ordered Jasmin to put her pajamas on. When Jasmin started to put them on the wrong way, the defendant beat her again with the extension cord. At one point, the defendant held Jasmin by her arm as he continued to beat her with the cord. In his confession, the defendant said that he beat the child on her arms, legs, back, stomach, chest, shoulders, and face. According to the defendant, the beatings occurred over the course of about an hour. Afterwards, the defendant helped Jasmin with her pajamas and put her to bed.
According to the defendant, Jasmin later complained that her head hurt, so the defendant placed a damp face towel on the child’s forehead. Sometime after that, Jasmin went to the bathroom and vomited several times. The defendant said that the child’s eyes were rolled upward in their sockets. Jasmin then returned to bed. She later needed to vomit again, and the defendant carried her into the bathroom. The defendant said that at one point he gave the chüd mouth-to-mouth resuscitation in an attempt to clear her nose and throat.
Pamela James returned around midnight, and the defendant told her that he had whipped Jasmin. By that time, Jasmin was no longer moving. There was no telephone in the apartment, so the defendant and Pamela left to summon help. Pamela called her father, Willie Davis, who lived about five blocks away. Davis and his wife came over immediately. Davis could not detect a pulse and found that the child’s body was cold. Davis and the defendant then left the apartment and flagged down a Chicago police officer. Jasmin was later transported by police vehicle to South Shore Community Hospital, where she was pronounced dead on arrival.
*9Detective Raymond Binkowski of the Chicago police department examined Jasmin at the hospital. Binkowski found bruises and abrasions on the child’s face, back, legs, buttocks, arms, and chest, and he directed an evidence technician to photograph the injuries. Detective Binkowski questioned the defendant around 3:30 a.m. on October 25; another officer, Detective William Kuschner, questioned Pamela James. According to Detective Binkowski, both the defendant and Pamela said in their initial interviews that it was Pamela who had whipped the child on October 24. Shortly after the defendant gave his initial statement, he consented to a search of the apartment. There, Detective Binkowski and a second officer found a belt and an extension cord on the top bunk of a bed, as defendant had indicated. The officers did not find evidence of blood or vomit in the apartment, or towels similar to the one defendant said he had placed on the child’s head. Later during the morning of October 25, the defendant made a formal, written statement, which was admitted into evidence at trial.
At trial the State also presented evidence of the autopsy performed on the victim on October 25, 1984, by Dr. Robert Stein, chief medical examiner of Cook County. The external examination of the victim revealed the presence of contusions on virtually every part of the child’s body, and that there were “too many to count.” Dr. Stein testified that the child’s injuries were consistent with blows inflicted from a belt, belt buckle, or electrical cord. He believed that most of the injuries were recent and were inflicted perhaps within moments of death. Other injuries were older, and could have been inflicted 30 to 45 minutes before death.
In his examination, Dr. Stein found contused areas under the child’s left eye and on the lower cheek. He also observed “punctated-like contused areas” on the left side of the nose. Dr. Stein testified that there were nu*10merous “spiral markings” on the child’s back, between the buttocks, just below the knee, and on both sides of the chest. Dr. Stein also found U-shaped contusions about 5 to 10 inches in length on the left side of the chest. Oval-shaped contusions were present on the upper portion of the left labia of the vagina and on the thigh of the left leg. Dr. Stein stated that he observed similar loop-like contusions on the child’s upper abdomen, the nipple of the right breast, the upper thigh of the right leg, the area just below the left collarbone, and the last rib of the chest. Dr. Stein also observed patterned markings on the buttocks, the back of the legs, and the groin area. Dr. Stein testified that all these injuries were consistent with blows from a belt or an electrical cord. Dr. Stein also found a number of curvilinear contusions consistent with blows from a belt buckle. Contusions of that type were present on the lower part of the child’s body, the legs, the right forearm, and the top of the left hand. Dr. Stein found .older contusions, which had healed, on the lower leg, and a swollen left shoulder.
Dr. Stein stated that an X ray of the child’s body revealed a recent fracture of the upper arm consistent with an upward pulling of the arm. He testified that an internal examination of the body revealed severe hemorrhage to the underlying fat and muscle. He noted that the amount and depth of the hemorrhage, particular in the area of the buttocks, indicated that the child’s injuries were severe. Dr. Stein also testified that he found a quantity of partially digested food in the child’s stomach, and that there was no evidence of vomit in the child’s mouth or nostrils. Dr. Stein concluded that death was not instantaneous but rather was the result of abuse inflicted over a protracted period of time.
The defendant testified at trial. He admitted whipping Jasmin on October 24, 1984, and his testimony was consistent with the confession he had given to the au*11thorities. The defendant denied, however, that at the time of the occurrence he had possessed any of the mental states necessary to sustain a charge of murder. The defendant specifically stated that he had not intended to kill the child or been aware that his actions created a strong probability of death. He explained that he whipped Jasmin because he was “mad with her because she had been disobedient.”
Pamela James also testified in behalf of the defendant. She said that she and other members of her family had whipped Jasmin with a belt when the child misbehaved. Pamela explained that she lied in her initial statement to the police, when she said that she had whipped the child on October 24. She explained, “I was scared because I wasn’t at home and something had happened to [Jasmin]. I didn’t know what had happened to her. So I lied.”
The trial judge found the defendant guilty of murder. The State then requested a capital sentencing hearing, and the defendant waived his right to a jury for purposes of the hearing. At the first phase of the hearing, certified copies of the defendant’s and Jasmin’s birth certificates were admitted into evidence. The parties stipulated that at the time of the offense the defendant was 27 years old and Jasmin was three years old. Following arguments by the parties, the trial judge determined that the defendant was eligible for the death penalty because the victim was under the age of 12 and was murdered in an exceptionally brutal and heinous manner indicative of wanton cruelty. See Ill. Rev. Stat. 1983, ch. 38, par. 9—1(b)(7).
The State presented one witness at the second stage of the sentencing hearing. Detective William Kuschner of the Chicago police department testified that he transported the defendant from the hospital to the police station around 2:15 a.m. on October 25. Detective Kuschner *12then remained with the defendant for some seven hours. Kuschner testified that the defendant appeared nervous during this time but did not cry or ask about Jasmin’s condition. Detective Kuschner also stated that the defendant initially lied about his participation in the child’s death, but that he later admitted that he alone had beaten the child on the evening of October 24.
The defendant presented a number of witnesses in mitigation at his sentencing hearing. Several relatives of the defendant testified in his behalf at the second stage of the sentencing hearing. They provided favorable views of the defendant, and attested to his good qualities. The defendant’s stepmother, Otha Lee Green, testified that the defendant, Pamela, and Jasmin lived with her for a period of time and that the defendant had treated Jasmin well. Mrs. Green also produced a set of children’s pajamas at the hearing. She stated that they were the pajamas worn by Jasmin on the night she died, and that Pamela had given them to her after the child’s funeral. According to Mrs. Green, the pajamas “had vomit on both sides and stool on the inside” when Pamela gave them to her. Mrs. Green said that she had not told defense counsel about the pajamas until after the trial.
Mary Tye, one of the defendant’s cousins, testified that defendant, Pamela, and Jasmin lived with her in the same household for a period of about six months. Mary Tye stated that the defendant did not abuse any of the children in the household during that time. Rosie Tye, an aunt of the defendant, testified that the defendant, Pamela, and Jasmin lived in her household for several months, and that the defendant seemed to be an ideal father to the little girl. Another aunt, Karlene Flournoy, testified that the defendant was well mannered as a child. The defendant's mother, Geraldine Tye, also testified in his behalf at the sentencing hearing. Mrs. Tye stated that she visited the defendant at the police station *13following his arrest and that he was crying and told her that he had not meant “to go that far” in disciplining Jasmin. The Reverend Charles Green, the defendant’s stepbrother, also testified. He said that the defendant “is a good man” and had shown concern for his family. The defendant also has helped Green perform maintenance on a building that Green owns. In addition to the evidence, the defendant made a statement to the court in allocution. The defendant declared that he had not intended to hurt or kill Jasmin, that he was only trying to discipline her, and that he did not realize he “put so many whelps on her.” At the conclusion of the hearing, the trial judge sentenced the defendant to death.
The defendant first contends that the evidence presented at trial was not sufficient to establish his guilt for the offense of murder. The defendant maintains that the State failed to prove that he acted with any of the mental states specified in the murder statute. The defendant insists that his conduct was only reckless, and he asks that his conviction be reduced to one for involuntary manslaughter.
On review, a criminal conviction will not be set aside on grounds of insufficient evidence unless the proof is so improbable or unsatisfactory that there remains a reasonable doubt of the defendant’s guilt. (People v. Collins (1985), 106 Ill. 2d 237, 261; People v. Williams (1982), 93 Ill. 2d 309, 315; People v. Vriner (1978), 74 Ill. 2d 329, 342.) “It is not our function to retry a defendant when considering a challenge to the sufficiency of the evidence of his guilt. (Collins, 106 Ill. 2d at 261.) Rather, determinations of the credibility of witnesses, the weight to be given to their testimony, and the reasonable inferences to be drawn from the evidence are responsibilities of the trier of fact. (People v. Brisbon (1985), 106 Ill. 2d 342, 360.)” (People v. Jimerson (1989), 127 Ill. 2d 12, 43.) In considering a defendant’s challenge to the suffi*14ciency of the evidence, “ ‘the relevant question is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.’ *** ‘[0]nce a defendant has been found guilty of the crime charged, the factfinder’s role as weigher of the evidence is preserved through a legal conclusion that upon judicial review all of the evidence is to be considered in the light most favorable to the prosecution.’ (Emphasis in original.)” (Collins, 106 Ill. 2d at 261, quoting Jackson v. Virginia (1979), 443 U.S. 307, 319, 61 L. Ed. 2d 560, 573, 99 S. Ct. 2781, 2789.) In the present case, we conclude that the evidence is sufficient to sustain the defendant’s conviction for murder.
The defendant in the present case was charged with the forms of murder defined in sections 9 — 1(a)(1) and (a)(2) of the Criminal Code of 1961 (Ill. Rev. Stat. 1983, ch. 38, pars. 9 — 1(a)(1), (a)(2)). The statute provides:
“A person who kills an individual without lawful justification commits murder if, in performing the acts which cause the death: '
(1) He either intends to kill or do great bodily harm to that individual or another, or knows that such acts will cause death to that individual or another; or
(2) He knows that such acts create a strong probability of death or great bodily harm to that individual or another.” (Ill. Rev. Stat. 1983, ch. 38, par. 9 — 1(a).)
Section 9 — 3(a) of the Criminal Code of 1961 provides, in pertinent part:
“A person who unintentionally kills an individual without lawful justification commits involuntary manslaughter if his acts whether lawful or unlawful which cause the death are such as are likely to cause death or great bodily harm to some individual, and he performs them recklessly ***.” (Ill. Rev. Stat. 1983, ch. 38, par. 9-3(a).)
*15Involuntary manslaughter is punishable as a Class 3 felony, and is not a capital offense. Ill. Rev. Stat. 1983, ch. 38, par. 9—3(b).
The defendant argues that the evidence presented at trial failed to establish that he intended to kill or cause Jasmin great bodily harm, or that he knew that his acts would cause death or would create a strong probability of death or great bodily harm to the child. The defendant maintains that the trial evidence shows only that he acted recklessly, and he therefore contends that he is guilty of no crime more serious than involuntary manslaughter. We believe that the evidence was sufficient to sustain the defendant’s conviction for murder.
The prosecution must prove every element of an offense beyond a reasonable doubt. (In re Winship (1970), 397 U.S. 358, 361-64, 25 L. Ed. 2a 368, 373-75, 90 S. Ct. 1068, 1071-73; People v. Kirilenko (1953), 1 Ill. 2d 90, 94.) The requisite mental state may be inferred from the defendant’s conduct and circumstances surrounding his commission of the crime. (People v. Terrell (1989), 132 Ill. 2d 178, 204; People v. Salazar (1988), 126 Ill. 2d 424, 449; People v. Bartall (1983), 98 Ill. 2d 294, 306-08.) In Bartall, the court explained, “[t]o prove the crime of murder, it is not necessary to show that the defendant has a specific intent to kill or do great bodily harm or that he knows with certainty that his acts will achieve those results.” (98 Ill. 2d at 307.) Rather, the necessary mental state may be inferred from evidence that the defendant “ ‘voluntarily and wilfully committed an act, the natural tendency of which was to destroy another’s life.’ (People v. Latimer (1966), 35 Ill. 2d 178, 182-83.)” (Bartall, 98 Ill. 2d at 307.) Disparity in size and strength between the defendant and the victim and the nature and extent of the victim’s injuries are relevant circumstances in ascertaining whether the defend*16ant possessed the necessary mental state. People v. Brackett (1987), 117 Ill. 2d 170, 179-80; People v. Ward (1984), 101 Ill. 2d 443, 451-52.
In the present case, the defendant was an adult male, and the victim was a three-year-old child. In beating the child, the defendant used first a belt and then an extension cord. According to the defendant’s own statement, the beating lasted about an hour. The injuries sustained by the child were severe and too numerous to count. Considering the disparity in size between the defendant and the victim, the brutality and duration of the beating, and the severity of the victim’s injuries, we conclude that the trial judge could infer that the defendant acted with the necessary mental state in bringing about the child’s death.
Citing Francis v. Franklin (1985), 471 U.S. 307, 85 L. Ed. 2d 344, 105 S. Ct. 1965, the defendant makes the related argument that our case law on this subject has created an impermissible presumption of intent or knowledge based on the severity of a beating. We do not agree. For example, in People v. Ward (1984), 101 Ill. 2d 443, this court upheld a murder conviction in a case involving the beating death of a four-year-old child. In that case, we held that the severity of the beating, coupled with the great disparity in size between the defendant and the victim, supported a finding that at the time of the beating the defendant possessed a mental state necessary to sustain conviction for murder. The court observed that “the severity of the beating negates any suggestion that [the defendant’s] conduct was only reckless.” (Ward, 101 Ill. 2d at 451.) Contrary to the defendant’s Anew, we do not consider that Ward created an impermissible presumption of intent or knowledge. The court’s decision in Ward turned on the particular evidence presented, as it must in every case of this nature. Nowhere in the decision did the court suggest that the *17prosecution was in some manner relieved of its burden of proving every element of the offense beyond a reasonable doubt.
The defendant next contends that the trial judge erroneously excluded certain testimony of Pamela James, who testified in behalf of the defendant at trial. On direct examination, Pamela described what occurred following her return to the apartment on the night of Jasmin’s death. On two occasions defense counsel attempted to elicit from Pamela testimony of what the defendant said while they were looking for a telephone from which to summon help. The character of the defendant’s supposed remarks is revealed by the leading question defense counsel asked the second time he raised the matter: “Is one of the things he said he said he didn’t know? He didn’t mean it and he just whipped her? Did he tell you that?” In both instances, the trial judge sustained the State’s hearsay objection to the testimony. In response to defense counsel’s argument that Pamela’s testimony was admissible as evidence either of the defendant’s state of mind or as part of the res gestae, the trial judge stated that he would allow the testimony only if it were offered as an admission. Defense counsel declined to offer it as such.
Before this court, the defendant contends that Pamela’s testimony was crucial in establishing the defendant’s mental state at the time of Jasmin’s death. According to the defendant, Pamela would have testified that the defendant said that he did not realize he was seriously injuring the child during the beating. The defendant argues that the testimony is admissible as an admission, as an excited utterance, or as a statement reflective of his mental state.
All three theories are problematic. The defendant’s trial counsel correctly declined to offer the testimony as an admission, for the statement was the defendant’s *18own, not that of a party-opponent; it was being offered in support of the defense contention that the defendant had not intended to harm the child. (See People v. Berry (1988), 172 Ill. App. 3d 256, 261; M. Graham, Cleary & Graham’s Handbook of Illinois Evidence §802.1, at 595 (5th ed. 1990).) At trial, defense counsel did not specifically invoke the excited utterance exception to the hearsay rule, relying instead on the more general, and disapproved, res gestae concept. (See People v. Poland (1961), 22 Ill. 2d 175, 180.) Assuming that counsel meant to offer the evidence under the excited utterance exception, we question whether the testimony would satisfy the requirement of that rule that there have been an absence of time in which to fabricate the statement. (See Poland, 22 Ill. 2d at 181.) Finally, the circumstances under which the statement was allegedly made do not indicate that it accurately reflected the defendant’s state of mind at the time of the occurrence. See Berry, 172 Ill. App. 3d at 262-63.
We need not decide here whether the testimony was admissible under any of the theories proposed by the defendant. As the trial judge explained in disposing of the same contention in the defendant’s post-trial motion, the error, if any, in. the exclusion of the testimony was harmless, given the other evidence in the record pertaining to the defendant’s mental state. In the present case, the defendant testified at trial, explaining that he did not intend to kill Jasmin or to cause her great bodily harm. He also stated that he had not known that death or great bodily harm were probable consequences of the beating he inflicted on the child. Pamela’s further testimony regarding the defendant’s alleged statement to her would have been cumulative of the evidence that was admitted, and we therefore conclude that any error in its exclusion was harmless. See People v. Bartall (1983), 98 Ill. 2d 294, 319.
*19We must also reject the related argument that the trial judge refused to consider the defendant’s own testimony concerning his state of mind at the time of the occurrence. In support of this contention, the defendant points to the trial judge’s statement, made at the time of the exclusion of Pamela’s testimony, that he would not consider that evidence. We construe that comment as indicating only that the judge would not consider the testimony counsel was attempting to elicit from Pamela. The trial judge excluded that portion of Pamela’s testimony because of the form in which it was offered, and the defendant failed at trial to propose a hearsay exemption or exception that would have warranted its admission. Nothing in the record suggests that the trial judge ignored competent evidence of the defendant’s mental state at the time in question. As we have discussed, in disposing of the defendant’s post-trial motion the judge expressly noted the evidence of record pertaining to the defendant’s state of mind. The judge’s comments at that time demonstrate that he was aware of the other testimony and that he had not disregarded it.
The defendant next argues that the trial judge improperly relied on his own background and experience in deciding to impose the death sentence in the present case. The defendant makes the related argument that his waivers of a jury for purposes of trial and sentencing were invalid because the judge failed to disclose those experiences to him, and he was not otherwise aware of them.
At the conclusion of the second phase of the sentencing hearing, the trial judge made the. following comments:
“In evaluating your acts I, as a jury, have a right, have a right to draw upon my experiences in life to determine how serious your crime was. And I’ll state for the record that for a period of seven years I was a homicide *20detective in the City of Chicago; and I investigated numerous child beatings. I investigated numerous child deaths. And I spent a total [of] 25 years in the criminal justice system. And I have never seen a child beaten with such viciousness, repeatedly beaten over an hour to the extent her death was caused.
Therefore, I’ve carefully considered the evidence in this case within the prescribed statutory framework, including the statutory factors in mitigation-aggravation. The presentence investigation, the credibility, and demeanor of the witnesses and of you and your deliberation and premeditation. And it is, therefore, the finding of this Court that there are insufficient mitigating factors to preclude the imposition of the death penalty. Pursuant to law if that’s my finding I must impose the death penalty.”
After the trial judge concluded his remarks, defense counsel immediately moved to vacate the death sentence, arguing that the judge had improperly relied on his personal background and experience in sentencing the defendant. The trial judge denied the motion.
The defendant argues that it was improper for the trial judge to rely on his experiences as a homicide detective, and on his knowledge of other child abuse cases, in determining whether to impose the death penalty in this case. The defendant also contends that his separate waivers of a jury for purposes of trial and sentencing were invalid because the judge failed to disclose those prior experiences, and because the defendant was not otherwise aware of the information. Because the focus of the defendant’s argument on this issue before this court concerns the role that the trial judge’s background and experience might have played in the decision to impose the death penalty in the present case, we shall consider that contention first, before turning to the defendant’s subsidiary arguments that his jury waivers were invalid.
*21We do not believe that the trial judge’s reference to his own background and experience in assessing the nature of the defendant’s crime denied the defendant a fair sentencing hearing. In Barclay v. Florida (1983), 463 U.S. 939, 77 L. Ed. 2d 1134, 103 S. Ct. 3418, the Supreme Court found no violation of the eighth amendment in the trial judge’s references to his own experiences in deciding to sentence the defendant to death. In that case, the trial judge discussed at length his experiences in the criminal justice system and as a serviceman during World War II, when he witnessed firsthand Nazi concentration camps and their victims. The judge then stated:
“ ‘Having set forth my personal experiences above, it is understandable that I am not easily shocked or moved by tragedy — but this present murder and call for racial war is especially shocking and meets every definition of heinous, atrocious and cruel.’ ” Barclay, 463 U.S. at 948 n.6, 77 L. Ed. 2d at 1143 n.6, 103 S. Ct. at 3424 n.6.
In Barclay, the defendant argued that the trial judge should not have considered his own experiences in deciding to impose the death penalty and that in doing so the judge had in effect relied on a nonstatutory aggravating circumstance. The defendant’s claim was rejected. The plurality noted that the trial judge’s experiences were relevant to several of Florida’s statutory aggravating circumstances, and that comparison of the defendant’s conduct with the Nazi concentration camps was “not an inappropriate way of weighing the ‘especially heinous, atrocious, or cruel’ statutory aggravating circumstance in an attempt to determine whether it warrants imposition of the death penalty.” (Barclay, 463 U.S. at 949, 77 L. Ed. 2d at 1144, 103 S. Ct. at 3424-25 (opinion by Rehnquist, J., joined by Burger, C.J., and White and O’Connor, JJ.).) The same plurality also stated:
*22“Any sentencing decision calls for the exercise of judgment. It is neither possible nor desirable for a person to whom the State entrusts an important judgment to decide in a vacuum, as if he had no experiences. The thrust of our decisions on capital punishment has been that ‘ “discretion must be suitably directed and limited so as to minimize the risk of wholly arbitrary and capricious action.” ’ [Citation.] ***
We have never suggested that the United States Constitution requires that the sentencing process should be transformed into a rigid and mechanical parsing of statutory aggravating factors. But to attempt to separate the sentencer's decision from his experiences would inevitably do precisely that. It is entirely fitting for the moral, factual, and legal judgment of judges and juries to play a meaningful role in sentencing. We expect that sentencers will exercise their discretion in their own way and to the best of their ability. As long as that discretion is guided in a constitutionally adequate way, [citation], and as long as the decision is not so wholly arbitrary as to offend the Constitution, the Eighth Amendment cannot and should not demand more.” Barclay, 463 U.S. at 950-51, 77 L. Ed. 2d at 1144,103 S. Ct. at 3425.
Justice Stevens, joined by Justice Powell, concurred in the Court’s judgment. Discussing the trial judge’s reference to his personal experiences, Justice Stevens wrote:
“[T]he judge’s candid exposition of his deeply felt concern about racial crimes had no bearing on any statutory aggravating circumstance, but in and of itself it does not undermine the legitimacy of the ultimate sentence. The sentencing process assumes that the trier of fact will exercise judgment in light of his or her background, experiences, and values. Just as sentencing juries ‘maintain a link between contemporary community values and the penal system,’ [citation],. sentencing judges ‘ “with experience in the facts of criminality posses[s] the requisite knowledge to balance the facts of the case against the standard criminal activity....” ’ [Citation.] Of course, if *23the criteria imposed by law are not satisfied in a particular case, a trial judge’s reactions based on his personal experiences cannot justify the death penalty. But that is not the case here.” (Barclay, 463 U.S. at 970-71, 77 L. Ed. 2d at 1157, 103 S. Ct. at 3435-36 (Stevens, J., joined by Powell, J., concurring in the judgment).)
Justice Stevens also explained why he believed that the trial judge’s concern over racial crimes, derived from the judge’s own experience, was relevant at sentencing, even if it was not directly related to a specific statutory aggravating circumstance. Justice Stevens stated, “This is not because it assisted the trial court in ‘weighing the “especially heinous, atrocious, or cruel” statutory aggravating circumstance,’ [citation], but because it pertained more generally to the trial judge’s exercise of his sentencing discretion — the third stage of the sentencing process.” Barclay, 463 U.S. at 970 n.18, 77 L. Ed. 2d at 1157 n.18,103 S. Ct. at 3435 n.18.
The separate opinions in Barclay demonstrate, we believe, that a sentencing authority’s decision whether to impose the death penalty need not be divorced from the sentencer’s own background and experience in life. Indeed, it is precisely that experience that grounds the decision in a particular case in the value system of the community. For these reasons, we find distinguishable Gardner v. Florida (1977), 430 U.S. 349, 51 L. Ed. 2d 393, 97 S. Ct. 1197, cited by the defendant. In Gardner, the sentencing judge made use of confidential portions of a presentence investigation report in deciding to impose the death penalty. The Supreme Court vacated the sentence, finding that the judge’s use of the material contained in the report rendered the sentencing decision unreliable. In the present case, and in Barclay, however, the sentencing authority did not make use of any additional, undisclosed information about the offense or the offender. Rather, the sentencing judge simply assessed *24the evidence in the context of his own experiences in life. To demand otherwise would, indeed, require that those decisions be made “in a vacuum.” (Barclay, 463 U.S. at 950, 77 L. Ed. 2d at 1144, 103 S. Ct. at 3425.) We conclude that the trial judge’s references to his. own background and experience in deciding to sentence the defendant to death were not inappropriate and do not require that the defendant be granted a new sentencing hearing.
We must also reject the defendant’s additional contention that the trial judge’s failure to reveal his experiences as a homicide investigator and his knowledge of other cases of child abuse vitiates the defendant’s waivers of his right to a jury for purposes of both the guilt-innocence and sentencing phases of the proceedings. As we explain below, we conclude that the defendant’s jury waivers were valid, and that the trial judge was not obligated to reveal his personal background to the defendant.
A jury waiver must be understanding^ made. (Ill. Rev. Stat. 1983, ch. 38, par. 103—6; People v. Smith (1985), 106 Ill. 2d 327, 334; People v. Taylor (1984), 101 Ill. 2d 508, 519-20; People v. Surgeon (1958), 15 Ill. 2d 236, 238.) Whether a waiver is knowing and intelligent will depend on the circumstances of the particular case. (People v. Buggs (1986), 112 Ill. 2d 284, 292; Taylor, 101 Ill. 2d at 520; People v. Lewis (1981), 88 Ill. 2d 429, 437-38.) Nothing in the record in the present case suggests that the defendant’s jury waivers were other than knowing and intelligent. Before trial, the court admonished the defendant of his right to a jury. The defendant responded that he understood what a jury trial is, and he expressly waived the right, signing a form to that effect. The defendant made a similar waiver before the beginning of the separate sentencing hearing.
*25A defendant has no right to demand a voir dire examination of the court so that he may decide whether to waive a jury. We consider it unnecessary, and impractical, to ground the validity of a jury waiver on the trial judge’s exposition of every aspect of his personal background that might somehow influence a defendant’s decision whether or not to submit his case to the judge alone. A defendant’s choice between a bench trial and a jury trial may depend on an infinite variety of circumstances. A potential juror with the same background and experience as the trial judge in the case at bar would not be automatically disqualified from service. Indeed, a juror may consider the evidence presented at trial in the light of the juror’s “own observations and experience in life.” (Illinois Pattern Jury Instructions, Criminal, No. 1.01[10] (2d ed. 1981); Illinois Pattern Jury Instructions, Civil, No. 1.04 (3d ed. 1990).) There is no reason to prevent a judge from also doing so. Background and experience are disqualifying only if they prevent a person from assessing the evidence fairly and impartially.
It is assumed that judges, regardless of their personal backgrounds and experiences in life, will be able to set aside any biases or predispositions they might have and consider each case in-light of the evidence presented. (See, e.g., People v. Davis (1983), 95 Ill. 2d 1, 24.) As this court stated in People v. Vance (1979), 76 Ill. 2d 171, 179:
“Every human is, consciously or subconsciously, partial to some degree in that he is influenced by the habits he has been trained in, the experiences he has had, occupationally or otherwise, the people with whom he associates, the area in which he lives and the innumerable unrecognized factors which subconsciously affect every individual’s philosophy. *** This, however, is nothing more nor less than one of the characteristics of human nature. The most that ought to be expected is that the judge will recognize that he has basic predilections and make a consci*26entious effort to set them aside and give dispassionate consideration to the case before him.”
It is further assumed that a judge, in a bench proceeding, considers only competent evidence in making a finding. (People v. Gilbert (1977), 68 Ill. 2d 252, 258; People v. Harris (1974), 57 Ill. 2d 228, 231; People v. Pelegri (1968), 39 Ill. 2d 568, 575.) This assumption will be overcome only if the record affirmatively demonstrates the contrary, as where it is established that the court’s finding rests on a private investigation of the evidence, or on other private knowledge about the facts in the case. (Gilbert, 68 Ill. 2d at 258-59; People v. Wallenberg (1962), 24 Ill. 2d 350, 354.) There is no indication in the present case that the judge’s determinations rested on his private investigation of the facts and circumstances of the case.
As we have explained, the trial judge could legitimately refer to his own background and experience in assessing the nature of the defendant’s offense and in determining whether to impose the death penalty. We also conclude that the defendant’s jury waivers at both the guilt-innocence and sentencing phases of the proceedings below were not rendered invalid by the trial judge’s failure to reveal to the defendant his personal background and experience.
The defendant next contends that death is not an appropriate sentence in the present case. The defendant maintains that his personal background and the circumstances of his offense “do not bespeak a man with a mar lignant heart who must be permanently eliminated from society.” (People v. Carlson (1980), 79 Ill. 2d 564, 590.) The defendant therefore asks that we vacate his death sentence and remand the cause for imposition of a sentence other than death.
We will vacate a death sentence that is excessive, or inappropriate, in light of the facts and circumstances of *27the particular case. (See People v. Johnson (1989), 128 Ill. 2d 253; People v. Buggs (1986), 112 Ill. 2d 284; People v. Gleckler (1980), 82 Ill. 2d 145; Carlson, 79 Ill. 2d 564. See also People v. Crews (1969), 42 Ill. 2d 60 (decision under former law).) As we explain below, we cannot conclude from our review of our prior cases, and of the record in the present case, that the defendant’s sentence is excessive.
In Johnson, the defendant was sentenced to death for the murder of an employee of a tire store where the defendant had recently been discharged from employment; the store manager and another employee were injured in the occurrence. In ruling that the death sentence was excessive, this court noted that the defendant had committed only one prior offense, a misdemeanor, for which he had successfully completed a term of supervision. The court found further evidence of the defendant’s potential for rehabilitation in the favorable testimony of one of the victims, who urged that the defendant not be sentenced to death. Finally, the court noted that the defendant’s conduct was related to his recent loss of employment, and the emotional upset produced by that event. Johnson, 128 Ill. 2d at 281-82.
In Buggs, the defendant was sentenced to death for the murder of his wife and of one of his children. The defendant was in his forties, had served in the military, and did not have a prior history of serious criminal conduct. The defendant had a drinking problem, and he committed the offenses after arguing with his wife over her supposed infidelity. The court ruled that death was an excessive sentence, concluding that the defendant “would presumably be leading a life acceptable to our society” if it were not for “this marital disharmony and a dispute which triggered this tragic sequence of events.” Buggs, 112 Ill. 2d at 295.
*28In Gleekler, the defendant was sentenced to death for the murder of two teen-aged boys. In concluding that the sentence was excessive, the court noted that the defendant had “no criminal history, the personality of a doormat, and a problem with alcohol.” (Gleckler, 82 Ill. 2d at 171.) In addition, the court applied a limited form of proportionality review in determining that the defendant’s sentence was excessive. The court believed that the defendant’s conduct was less culpable that the conduct of a codefendant who had been sentenced to prison for the same offenses and that the defendant's rehabilitative potential was not demonstrably worse than his codefendant’s. Gleckler, 82 Ill. 2d at 171.
In Carlson, the defendant was sentenced to death for the murder of a police officer. The defendant had killed his wife earlier the same day and fatally shot the officer in an attempt to avoid arrest for the other murder. This court held that death was an excessive sentence. The court noted that the defendant was in his early forties, did not have a prior record of criminal conduct, had been in ill health, and was upset over his former wife’s plans to remarry. The court also noted that, at the time of the officer’s murder, the defendant was attempting to relay money to his son to provide for the child’s support. The court believed that the defendant “would in all probability be leading a life acceptable to our society had not his unfortunate marital affair triggered this tragic sequence of events.” Carlson, 79 Ill. 2d at 590.
In Crews, a decision under former law, the defendant was sentenced to death for the murder of a two-year-old girl. Like the victim in the present case, the victim in Crews died as a result of a beating. In vacating the death sentence in that case, the court noted that the defendant, a 34-year-old woman, did not have a prior criminal record, that the defendant had'previously “expressed extreme anxiety about her ability to care for” *29the victim, whom the defendant and her husband were planning to adopt, and that the defendant had been consuming excessive amounts of amphetamines, which would have reduced her capacity to control her emotions. Crews, 42 Ill. 2d at 65-66.
Imposition of the death penalty requires an individualized assessment of the circumstances and character of the offender and the offense. (Eddings v. Oklahoma (1982), 455 U.S. 104, 110-12, 71 L. Ed. 2d 1, 8-9, 102 S. Ct. 869, 874-75.) In deciding whether imposition of that sentence in a particular case is excessive, we will consider “whether the circumstances of the crime and the character of the defendant are such that the deterrent and retributive functions of the ultimate sanction will be served by imposing the death penalty.” Johnson, 128 Ill. 2d at 280.
The defendant argues that his conduct in the present case and his personal record and background are as favorable as the conduct and records of the defendants in the cases in which death sentences have been found to be excessive. The defendant correctly observes that he does not have a prior record of criminal activity. The defendant also notes that he is the father of four other children, apart from Jasmin and Alicia, his children by Pamela James. Characterizing the present offense as an “isolated and tragic episode,” the defendant submits that his actions were impulsive, occurring as he attempted to discipline a child, and the defendant adds that corporal punishment was a common feature of the households in which he grew up. For further evidence of mitigation, the defendant points to his conduct following Jasmin’s death: he attempted to summon help, he cried and was otherwise remorseful, and he cooperated with authorities, consenting to a search of his residence and confessing his role in the occurrence.
*30Death sentences were vacated as excessive in Johnson, Buggs, Gleckler, and Carlson because each of the defendants in those cases did not have a significant history of prior criminal conduct and because each of the offenses was precipitated by some stressful circumstance or other mental or emotional disturbance. The rationale common to those decisions was that imposition of the death penalty would not have served the deterrent and retributive purposes of capital sentencing. (See Gregg v. Georgia (1976), 428 U.S. 153, 183, 49 L. Ed. 2d 859, 880, 96 S. Ct. 2909, 2929-30 (plurality opinion).) And in Crews, a decision under former law, similar concerns led the court to vacate the defendant’s death sentence as excessive. Although the defendant in the present case did not have a history of prior criminal conduct, his actions here were triggered by nothing more serious than a three-year-old child’s refusal to go to bed when she was told to do so. Using a belt and an extension cord, the defendant beat the young girl for about an hour. According to the autoptic evidence, the child’s injuries were too numerous to count, and they were present over virtually her entire body. Marks that corresponded to the shape of a belt buckle were visible on her skin, and her arm was broken. The defendant was nearly 28 years old at the time of the occurrence. There was no claim, or evidence, that the defendant was laboring under an emotional or mental disturbance. Nor was there any evidence of drug or alcohol use, a circumstance that would not excuse, but might partially explain, the defendant’s conduct. (See Johnson, 128 Ill. 2d at 282 (“The defendant’s drugged and intoxicated condition on that day may partially explain his actions but it does not excuse them”).) The absence of any physical or mental condition that would account for the defendant’s actions underscores the brutality of the defendant’s conduct in the present case. From our review of the record in the present case, we *31cannot say that the defendant’s sentence is excessive, or inappropriate.
The defendant also challenges the facial validity of the statutory aggravating circumstance on which he was found eligible for the death penalty. Section 9—1(b)(7) of the Criminal Code of 1961 authorizes the imposition of the death sentence when “the murdered individual was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty.” (Ill. Rev. Stat. 1983, ch. 38, par. 9—1(b)(7).) The defendant contends that the terms used in the statute to define the conduct that will sustain a finding of eligibility — “exceptionally brutal or heinous behavior indicative of wanton cruelty” — are unconstitutionally vague and fail to satisfy the requirement of a valid death sentencing scheme that the discretion of the sentencer be adequately channeled. The defendant notes that this court, in People v. Odle (1988), 128 Ill. 2d 111, upheld section 9—1(b)(7) against a similar challenge, and he asks that we reconsider that decision.
In Maynard v. Cartwright (1988), 486 U.S. 356, 100 L. Ed. 2d 372, 108 S. Ct. 1853, the Supreme Court found that language in an Oklahoma statutory aggravating circumstance permitting imposition of the death penalty in instances of “especially heinous, atrocious, or cruel” conduct did not adequately limit the discretion of sentencers, in accordance with the requirements of the eighth amendment. (Maynard, 486 U.S. at 364-65, 100 L. Ed. 2d at 382, 108 S. Ct. at 1859-60. See also Godfrey v. Georgia (1980), 446 U.S. 420, 64 L. Ed. 2d 398, 100 S. Ct. 1759 (invalidating “outrageously or wantonly vile, horrible or inhuman” aggravating circumstance of Georgia death penalty statute).) In light of the decision in Maynard, this court has since considered the analogous provision in section 9—1(b)(7). We have decided that the statutory language, as interpreted, sufficiently chan*32neis the discretion of the sentences (People v. Lucas (1989), 132 Ill. 2d 399, 443-46; People v. Terrell (1989), 132 Ill. 2d 178, 224; People v. Kidd (1989), 129 Ill. 2d 432, 454-56; People v. Odle (1988), 128 Ill. 2d 111, 138-41.) As this court determined in Lucas, the terms used in section 9 — 1(b)(7) have been construed in other contexts as involving the infliction of prolonged pain or torture, or premeditated behavior on the part of the defendant, and it is on those bases that the aggravating circumstance should be applied. (Lucas, 132 Ill. 2d at 445-46.) With that construction, adequate guidance is given to the sentences
We are aware, of course, that the trial judge did not have the benefit of that construction when he decided whether the present defendant should be sentenced to death. (Cf. Walton v. Arizona (1990), 497 U.S. 639, _, 111 L. Ed. 2d 511, 528, 110 S. Ct. 3047, 3057 (unlike jury, judge presumed to be aware of narrowing construction adopted by reviewing court).) The defendant’s sentencing hearing was conducted in May 1986, predating our decisions in Odie and Lucas by several years. The defendant does not ask, however, that the present action be remanded to the circuit court for reconsideration in light of the Odle-Lucas limiting construction, and we do not believe that such action would be warranted here. As we have said, the trial judge referred to the viciousness of the beating and to the protracted period over which it was inflicted. Applying the Odle-Lucas limiting construction to the evidence presented in this case, we conclude that the aggravating circumstance was established, and that the defendant was therefore eligible for the death penalty.
Finally, the defendant raises a series of challenges to the facial validity of the Illinois death penalty statute (Ill. Rev. Stat. 1983, ch. 38, par. 9— 1), arguing that the provision is, for various reasons, unconstitutional under *33the eighth and fourteenth amendments (U.S. Const., amends. VIII, XIV). As indicated below, the same contentions have previously been considered and rejected, however, and the defendant has presented us with no persuasive ground that would justify reconsideration of any of those rulings.
The statute is not invalid for the discretion it allows the prosecutor in deciding whether or not to seek the death penalty in a particular case. (Silagy v. Peters (7th Cir. 1990), 905 F.2d 986, 993-94; People v. Lewis (1981), 88 Ill. 2d 129, 146; People ex rel. Carey v. Cousins (1979) , 77 Ill. 2d 531, 534-43.) The statute does not unconstitutionally cast on the defendant the burden of establishing that a sentence other than death should be imposed in his case (Silagy, 905 F.2d at 998-99; People v. Orange (1988), 121 Ill. 2d 364, 390; People v. Caballero (1984), 102 Ill. 2d 23, 49), nor is the statute invalid for failing to impose on the State a burden of persuasion at the second phase of the sentencing hearing (People v. Jones (1988), 123 Ill. 2d 387, 426; People v. Eddmonds (1984), 101 Ill. 2d 44, 68; People v. Free (1983), 94 Ill. 2d 378, 421). The Federal Constitution does not require proportionality review in capital cases (Pulley v. Harris (1984), 465 U.S. 37, 79 L. Ed. 2d 29, 104 S. Ct. 871), and the absence of a mechanism for that type of review does not render the Illinois statute invalid. (Silagy, 905 F.2d at 1000; People v. King (1986), 109 Ill. 2d 514, 551; People v. Stewart (1984), 104 Ill. 2d 463, 499; People v. Kubat (1983), 94 Ill. 2d 437, 502-04; People v. Brownell (1980) , 79 Ill. 2d 508, 531-34.) Nor is the Illinois statute invalid because it fails to require the sentencer to make a separate finding that death is the appropriate penalty. People v. Whitehead (1987), 116 Ill. 2d 425, 462-63; People v. Guest (1986), 115 Ill. 2d 72, 112; People v. Morgan (1986), 112 Ill. 2d 111, 147.
*34For the reasons stated, the defendant’s conviction and sentence are affirmed. The clerk of this court is directed to enter an order setting Thursday, March 14, 1991, as the date on which the sentence of death, entered in the circuit court of Cook County, is to be carried out. The defendant shall be executed by lethal injection in the manner provided by section 119 — 5 of the Code of Criminal Procedure of 1963 (Ill. Rev. Stat. 1989, ch. 38, par. 119 — 5). The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, to the warden of Stateville Correctional Center, and to the warden of the institution where the defendant is currently confined.
Judgment affirmed.