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Note that by using just 7 bits, you can represent all the decimal numbers from 0 to 127, which is a total
of 2 7 , or 128 numbers; and using all 8 bits you get 256, which corresponds to 2 8 numbers. In general, if you
have n bits available, you can represent 2 n positive integers with values from 0 to 2 n 1 . Of course, I am only
talking in the context positive numbers so far. If you also need the same number of negative numbers, you
need more bits. I get to negative numbers in a moment.
When you get to work with larger binary numbers — for example, numbers with 24 bits:
1111 0101 1011 1001 1110 0001
the notation starts to be a little cumbersome, particularly when you consider that if you apply the method you
saw in the previous section to work out what this is in decimal notation, it's only 16,103,905, a miserable 8
decimal digits. You can sit more angels on a pinhead than that. Well, as it happens, you have an excellent
alternative.
Arithmetic to base 16 is a very convenient option. Numbers to base 16 are hexadecimal numbers. Each
digit can have values from 0 to 15 (the digits from 10 to 15 being represented by the letters A to F as shown
in Table B-2 , or by a to f if you're averse to capitalization) and values from 0 to 15 correspond quite nicely
with the range of values that four binary digits can represent.
TABLE B-2: Base 16 Conversion Table
0
0
0000
1
1
0001
2
2
0010
3
4
0011
4
4
0100
5
5
0101
6
6
0110
7
7
0111
8
8
1000
9
9
1001
A
10
1010

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