| The basic basis of bases
The base of a number system is the number of different symbols used
in it. In the case of the denary system, we use 10 different symbols, 0
. . . 9, other numbers, like 28657, are simply combinations of the 10
basic symbols.
Since the denary system uses 10 digits, the system is said to have a base of 10. The base is therefore just the technical word for the number of digits used in any counting system.
Counting with only two figures
We can count using any base that we like. In the denary or decimal
system, we used a base of 10 but we have seen that microprocessors
use a base of 2 - just the two digits 0 and 1. This is called the binary
system.
We usually abbreviate the words BInary digiT to bit.
Counting follows the same pattern as we have seen in the denary system: we use up the digits then start again.
Let’s give it a try. Start by listing all the digits:
0
1
and that’s it!
We now put a ‘1’ in the next column and start again:
10
11
It is convenient at this stage to keep the number of binary columns
the same and so we add a 0 at the start of the first two digits. These
extra zeros do not alter the value at all. For example, the denary
number 25 is not affected by writing it as 025 or 0025 or even
000 000 000 000 025.
The binary and decimal equivalents are:
Binary Denary
00 0
01 1
10 2
11 3
Binary - the way micros count
We do the same again - put a ‘1’ in the next column and repeat the pattern to give:
Binary Denary
100 4
101 5
110 6
111 7
and once more:
Binary Denary
1000 8
1001 9
1010 10
1011 11
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