Is Cao Cao from Han Dynasty or Wei State? Is Si Mazhao Wei and Jin Dynasties?

Cao Cao (155-220) was born in Azhen Mengde, Han nationality and Peiguoqiao (now Bozhou, Anhui). A famous politician, strategist, writer and calligrapher in the late Eastern Han Dynasty.

Si Mazhao (2 1 1-265) was born in Wen Ren, Hanoi (now Wenxian County, Henan Province). The second son of Sima Yi. Politicians and militarists in the late Cao and Wei Dynasties of the Three Kingdoms

Is it because Cao Cao spanned the Eastern Han Dynasty and Si Mazhao experienced the Three Kingdoms and the Western Jin Dynasty? Isn't it clear how to determine their time? Cao Cao must be in the Three Kingdoms period: after Cao Cao died in Luoyang, Cao Pi, the son of Cao Cao, forced Emperor Xian of Han to abdicate and usurp the Han regime, and became emperor in Luoyang, and Cao Wei was established. Cao Wei was initiated by Cao Pi, and Cao Cao was already dead. As for Si Mazhao, although he was "Emperor Wen of the Western Jin Dynasty", it was his son Sima Yan who claimed to be Emperor Wen after he proclaimed himself emperor, so Si Mazhao was gone in the Western Jin Dynasty.

Therefore, Cao Cao was born in the late Eastern Han Dynasty (before the establishment of Wei State), and Sima Zhao was born in the Three Kingdoms period.