Count after me

At primary school in the 1960s, our head-teacher was well aware of the digital revolution that had started. They were a maths enthusiast and, at age 9 or 10, we were taught how to do basic arithmetic using different 'bases'. Everyday base 10, of course, but also base 3, that only uses digits 0-2, base 4 (0-3) and, ultimately base 2 - binary, the digital 'language' - which only uses digits 0 and 1. Comparing base 10 with binary:

1 = 1
2 =10
3 =11
4 = 100
5 = 101 and so on

When our teacher thought we had got the hang of things, they blew our minds by introducing the idea of 'base 16' - hexadecimal. This uses a single digit to represent all the values from zero to fifteen, then sixteen is written as '10'. Hexadecimal ('hex' to all computer nerds) needs single digits to represent the numbers between ten and fifteen. By convention, the letters A-F are used, so simple counting in hex goes: 1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10,11....19,1A,1B,1C,1D,1E,1F,20 and so on

In computing, there is an intimate relationship between binary and hexadecimal notation. Computer data is stored in billions of minute switches that are 'on' or 'off'. These states are represented by 1 and 0, so digital data is represented as binary numbers - strings of 0s and 1s. It is very unwieldy to view or print numbers in this form but, luckily, binary numbers can be easily converted into hexadecimal numbers. This is because any four-character binary number can be converted into a single hex character.

The maximim value of a four-character binary number is 1111 - equal to fifteen. Hex for fifteen is 'F'. Any other four-character binary is something between 0 and E. An eight-character binary number becomes a two-character hex; twelve becomes three, sixteen becomes four and so on. Digital data becomes much more magageable and readable. There are people who can read and interpret hex script in their head!

The Sumerian people occupied cities in the middle-east from about 5500 years ago. Around 5000 years ago they created the 'cuneiform' alphabet and began writing things down. Cuneiform script included a numbering system that I read today was in "base 60"!! This suggests that all the values from one to fifty-nine are represented by a single character - and not until reaching the value sixty do you employ the next 'column' with a number analogous to '10'

Digging a bit deeper, I found it was both simpler and more complex. They actually had characters representing one to nine, along with other characters representing ten, twenty, thirty, forty, and fifty. Combining these characters let them represent any number up to fifty-nine in a single 'column'. For any larger numbers, they started using columns, just as we do now. But a 'one' in the second column represented not ten, but sixty; a 'two' represented not twenty but one-hundred-and-twenty, and so on. It seems very alien, but it's logical and it works. It was used by the Sumerians, and their successors they Babylonians, for many centuries. If you have ever wondered why there are 60 minutes in an hour, it's down to them

On a very wet evening in the West Midlands, all numbers mean 'Birmingham'