Were Al-Biruni and William the Conqueror alive at the same time?
Yes. Al-Biruni and William the Conqueror were alive at the same time, from 1027–1028 to 1048.
Al-Biruni
11th-century Persian scholar and polymath
Born 4 September AD 973 · died 9 December 1048, aged 75
William the Conqueror
King of England from 1066 to 1087, Duke of Normandy from 1035 to 1087
Born 1027–1028 · died 9 September 1087