Encoding Numbers

We count with 10 digits; 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9.

The highest number you can count to using just one decimal digit is 9.

If we try to go higher we will run out of digits. The solution when we run out of digits is to stick a column in front of the first, put a 1 in it and start again, so after 9 comes 10, after 99 comes 100 after 999 comes 1000 and so on.

We are taught how to count this way at primary school when we learn units, tens, hundreds and thousands.

This is the decimal system.

The binary system only has two digits; 0 & 1.

The highest number you can count to using just one binary digit is 1.

If we try to go higher we will run out of digits. The solution when we run out of digits is to stick a column in front of the first, put a 1 in it and start again, so after 1 comes 10, after 11 comes 100, after 111 comes 1000 and so on.

If we counted using binary we would have been taught units, twos, fours and eights at primary school!