Question

Convert the decimal expansion of each of these integers to a binary expansion.
a.321
b.1023

Answer 1

$321=256+64+1=2^8+2^6+2^0\implies321_{10}=101000001_2$

$1023=1024-1=2^{10}-2^0\implies1023_{10}=10000000000_2-1_2=1111111111_2$