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الكلية كلية الهندسة
القسم الهندسة الكهربائية
المرحلة 1
أستاذ المادة مراد عبيد حلو العجيلي
4/13/2011 8:37:10 AM
Frequently there is a need for a decimal output even though digital machines operate
in pure binary. As a result at the interface between a digital device and the outside
world facilities must be provided to convert pure binary to a decimal representation.
In practice, for example, calculators have been designed to work entirely in a decimal
mode. In such cases decimal digits are represented by a string of binary digits referred
to as a code. Four bits are required to represent the ten decimal digits, and since there
are 24 combinations of four binary digits, six combinations are not used and the code is
said to contain redundancy.
The four binary digits can be allocated to ten decimal digits in a purely arbitrary
manner and it is possible to generate 2.9 • 101~ four-bit codes, only a few of which
have any practical application. The most common group of codes for representing
decimal numbers are weighted and there are 17 of these codes. For this group of codes
the sum of the weights must be > 9 < 15 and examples of four of them are given in the
tabulation shown in Figure 1.10.
Of this group the most commonly used weighted code is naturally binary coded
decimal (NBCD) which uses the first ten combinations of the 4-bit binary count from
0000 to 1001 inclusive. The code weighting for NBCD is 8, 4, 2, 1 and this can be used
to find the corresponding decimal value of a given code. For example"
1001 = 8 x 1 + 4 x 0 + 2 x 0 + 1 x 1 = (9)10
Weighted codes having some negative weights are also available. Such a code
is the 8, 4, -2,-1 which, like the 2, 4, 2, 1 code, has the useful property of
self-complementation. By complementing each of the bits of a given codeword,
a new codeword is formed which represents the 9 s complement of the decimal
digit represented by the original codeword. For example, in the 8, 4, -2, -1 code
01 l0 represents (2)10 and, after self-complementation, 1001 represents (7)10 which
is the 9 s complement of (7)~0. Another example of a self-complementing code is
the XS3 code. This is not a weighted code but contains combinations of natural
binary in the range (3)10 to (12)10. The decimal value allocated to each binary
code is defined to be 3 less than its actual value. For example, (1)10 is represented
by 0100.
Decimal
digit
0
1
2
3
4
5
6
7
8
9
NBCD
8,4,2,1
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
BCD
7,4,2,1
0000
0001
0010
0011
0100
0101
0110
1000
1001
1010
BCD BCD
2,4,2,1 8,4,-2,-1
0000
0001
0010
0011
0100
1011
1100
1101
1110
1111
0000
0111
0110
0101
0100
1011
1010
1001
1000
1111
Figure 1.10 Binary codes for the decimal digits
Excess 3
XS3
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
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