Information Representation
 Number Base - Weights

In the Decimal system, when we write a number like 5837, we know it means "five thousand, eight hundred, and thirty-seven" The first digit is the number of thousands (103), the second is the number of hundreds (102), the third is the number of tens (101), the last is the number of units (100). We could put our number 5837 in a table with each digit in a column under its power of ten. See the table below.

 103 102 101 100 5 8 3 7

The powers of ten indicate the 'weight' of a column.

We could add to this table the numbers 0,1,2,3 to number the columns according to their power, and we could also add the value of the number base raised to that power. Again, see the table below.

 Weight 103 102 101 100 Digit position no. 3 2 1 0 Column value 1000 100 10 1 Value multiplier 5 8 3 7

So the value of a number expressed as a sequence of digits is dependent upon the number base being used, the symbols used in that system and the base raised to the power of the digit's position number.

When we count in the Decimal system we count 0,1,2,3.....9, then we reset the units value to 0 and carry 1 to the tens column. In the Octal system we count 0,1,2,.....7, then we reset to 0 and carry 1. In the Binary system we count 0,1 then we reset to 0 and carry 1. In the Hexadecimal system we count 0,1,2 ..... 9,A,B,C,D,E,F, then we reset and carry 1. Here the letters allow us to count up to 15 in our first column without having to carry.