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8th October 2016

Converting to Binary

To convert 87 to binary:

0	1	2	5	10	21	43	87
0	1	0	1	0	1	1	1
128	64	32	16	8	4	2	1

The trick here is that (working right to left) you keep halving the number (round down if odd) until you get to 1, and then mark any odd numbers as "1", and any even numbers as "0". This gives you 01010111, or 87.

To break it down in a little more detail:

1.	87 / 2 = 43 (rounding down). 87 is odd, so leave a 1.	_______1
2.	43 / 2 = 21 (rounding down). 43 is odd, so leave a 1.	______1_
3.	21 / 2 = 10 (rounding down). 21 is odd, so leave a 1.	_____1__
4.	10 / 2 = 5. 10 is even, so leave a 0.	____0___
5.	5 / 2 = 2 (rounding down). 5 is odd, so leave a 1.	___1____
6.	2 / 2 = 1. 2 is even, so leave a 0.	__0_____
7.	1 / 2 = 1. 1 is odd, so leave a 1, and finish, as we've got down to 1.	_1______
8.	Anything else is zero; you can add an 8th line to make it up to a full byte.	0_______
Answer - The top result goes on the right, the bottom is on the left:		01010111

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