The pure binary system discussed above is more appropriate for scientific applications where the bulk of work consists of arithmetic computations. Business applications entail reading and writing of voluminous amount of plain English, viz., names and address of customers and suppliers, employees, descriptions of stock items, etc. and comparatively less arithmetic. Therefore, most business computers employ a version of the pure binary system, the BCD system that is a hybrid of the pure binary system and the decimal system.
In this system, the decimal weighting is maintained, but the digit is represented by a combination of the binary digits 0 and 1. Since ten digits 0….9 have to be represented, a minimum of four bits must be used to encode each digit. Hence, each digit is represented by its binary equivalent using four bits, e.g., the digit 5 is equivalent to binary 0101 and the digit 9 is equivalent to binary 1001. By this method, the number 59 is represented as 0101 1001. The pure binary equivalents of the decimal digits 0 through 9 are given in Table 2.2 below.
Digit Pure Binary Equivalents
(or BCD’s)
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
The BCD equivalents of longer numbers are simply derived by appropriate juxtaposition of the equivalents in the above table. For example, the BCD equivalent of 951 is got by juxtaposing the individual equivalents of 9, 5 and 1 from this table as below:
BCD equivalent of 951 : 1001 0101 0001.
This codification scheme has been extended to cover the alphabetsand special symbols by adding two more bits (known as the zone bits) on the left of the 4 bit sets in the above table. By permuting the two zones bits, the representations for alphabets and special symbols as shown in Table. 2.3 can be obtained, those for the alphabets as hereunder:
Character BCD representation Character BCD representation
0 00 0000 J 10 0001
1 00 0001 K 10 0010
2 00 0010 L 10 0011
3 00 0011 M 10 0100
4 00 0100 N 10 0101
5 00 0101 O 10 0110
6 00 0110 P 10 0111
7 00 0111 Q 10 1000
8 00 1000 R 10 1001
9 00 1001
A 11 0001
B 11 0010 S 01 0010
C 11 0011 T 01 0011
D 11 0100 U 01 0100
E 11 0101 V 01 0101
F 11 0110 W 01 0110
G 11 0111 X 01 0111
H 11 1000 Y 01 1000
I 11 1001 Z 01 1001
With the 6 bits, it is possible to have 2 6 = 64 codes and this suffices to represent all the digits (10), alphabets (26, only upper case) and special symbols (around 15).