Denary to Binary: Repeated Division Method

Repeated division is a way of turning a denary number into binary by dividing by 2 again and again. You divide by 2, write down the remainder, and keep dividing the whole-number answer until it reaches 0.

Working through 45

Divide 45 by 2 and note the remainder — the 0 or 1 left over. Then divide the whole-number answer (the quotient) by 2 and note that remainder too. Stop as soon as the quotient reaches 0, because there is nothing left to halve.

Read the remainders backwards

The remainders arrive the wrong way round: the first one you find is the least significant bit, which belongs on the far right of the answer. So read the list from the bottom upwards: 1 0 1 1 0 1. That gives 101101, and 32 + 8 + 4 + 1 = 45, which checks the answer is correct.

Pad to exactly eight bits

101101 is only six bits long, so add leading zeros on the left until you have eight bits: 0010 1101. The zeros add no value, but they keep every bit sitting in the correct place value column. Smaller numbers need more padding — denary 5 comes out as 0000 0101 — while values of 128 or more already fill all eight places.