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Table 4.2 Numbering Systems
Binary
Decimal
0
0
0
1
1
1
10
2
2
11
3
3
100
4
4
101
5
5
110
6
6
111
7
7
1000
8
8
1001
9
9
1010
10
A
1011
11
B
1100
12
C
1101
13
D
72
1110
14
E
1111
15
F
Each of the binary values is called a bit. A group of bits is called a byte. In Table 4.2, the largest
binary value is a 4-bit byte. Computers are arranged in dif erent types of bytes, and the 8-bit
byte is commonly used as a general reference to a byte. However, modern computers are
actually organized into 8-, 16-, 32-, 64-, and even 128-bit bytes. (h ey just keep getting bigger,
so don't expect 128-bit bytes to be the top limit.)
h e highest value for a binary counting system in an 8-bit byte is 11111111. When you look at
that compared with decimal and hexadecimal numbers, you see a very interesting pattern, as
shown in Table 4.3.
Table 4.3 Byte Values
Binary
Decimal
Hexidecimal
11111111
255
FF
As you can see in Table 4-3, the hexadecimal value FF is the highest possible value for two
digits; similarly, the binary value 11111111 is the highest possible value for eight digits (a
byte). However, the decimal number is three digits and does not represent a limit for those
digits. In other words, the decimal system isn't very symmetrical with the binary counting
system, but the hexadecimal system is.
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