Binary, denary, hexadecimal, BCD and prefixes

Last time

Before we start: last time, in File sizes, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Why computers count in twos

A light switch is on or off. Billions of tiny switches inside a processor do the same, so every number a computer stores is a pattern of ones and zeros. Hexadecimal is the shorthand people use to read those long patterns, and BCD is a special way to store each decimal digit separately.

Place values in binary

In binary, the columns are worth one, two, four, eight, sixteen, thirty-two, sixty-four and one hundred and twenty-eight. To convert binary to denary, add up the columns that hold a one. The number one zero one one one zero one zero has ones in the columns for 128, 32, 16, 8 and 2. That is one hundred and twenty-eight plus thirty-two plus sixteen plus eight plus two: one hundred and eighty-six.

Denary to binary

To go the other way, start with the biggest column that fits. For 186, take 128 and write a one. The remainder is fifty-eight. The next column, 64, is too big, so write a zero. Thirty-two fits: write one, leaving twenty-six. Sixteen fits, leaving ten. Eight fits, leaving two. Four does not fit, two does, and one does not. The binary number is one zero one one one zero one zero.