NECO 2022 · Paper 1 · Q15

Simplify $110011_{\text{two}} \times 101_{\text{two}}$ .

Worked solution (try it first)

Convert to base ten: $110011_{\text{two}} = 32 + 16 + 2 + 1$
$= 51$ and $101_{\text{two}} = 5$ .
Multiply: $51 \times 5 = 255$ .
$255 = 256 - 1 = 2^8 - 1$ , which is eight 1s in base two: $11111111_{\text{two}}$ , option A.