WAEC 2009 · Paper 2 · Q6✱

(a)
By how much is $11000_2$ greater than or less than $111_2 \times 11_2$ ? Give your answer in base two.
Model answer
$111_2 \times 11_2 = 10101_2$ and $11000_2 - 10101_2 = 11_2$ , so $11000_2$ is greater by $11_2$ (3 in base ten).
(b)
A shopkeeper has 20 television sets in stock. He sells 18 of them at a profit of 15% and the remaining two at a loss of 5%. Find his percentage profit on the 20 sets.

Worked solution (try it first)

Multiply in base two: $111_2 \times 11_2 = 111_2 \times 10_2 + 111_2$
$= 1110_2 + 111_2$
$= 10101_2$ .
Subtract: $11000_2 - 10101_2 = 11_2$ (check in base ten: $24 - 21 = 3$ ).
So $11000_2$ is greater by $11_2$ .