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2.3.1 BCD (Binary Coded Decimal)
BCD is the oldest coding system where each decimal digit is expressed as a group of 4 bits or nibbles. These 4-bit binary
numbers have their weights attached as 8, 4, 2, and 1 from MSB to LSB. The BCD equivalent of decimal digits from 0 to
9 are represented in the following table.
Decimal digit BCD equivalent
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
To represent the BCD of multi-digit numbers, we have to convert each digit to its BCD equivalent. For example, the
decimal number 10 has two digits 0 and 1. BCD of 0 is 0000 and 1 is 0001. So, 10 when converted to BCD will be
00010000.
Example 1: Write the BCD representation of 255.
2 5 5
0010 0101 0101
So, the BCD equivalent of 255 is 001001010101.
The reverse conversion, i.e., BCD to decimal is similar. We have to make a group of 4 bits starting from the rightmost
bit and write the corresponding decimal equivalent from the above table.
Example 2: Write the decimal representation of 1001100001100011.
Grouping in 4 bits and writing the decimal equivalent of each group:
1001 1000 0110 0011
9 8 6 3
So, the equivalent decimal number is 9863.
Application of BCD:
• BCD systems are used in electronic counters, digital clocks, and pocket calculators.
Limitations of BCD:
• BCD codes are inefficient as compared to binary codes. For example, 12 in binary is 1100 but in BCD notation it is
written as 0001 0010.
• Arithmetic operations become more complex as compared to binary notation.
• As BCD is a 4-bit code, it can only represent numbers and is incapable of handling non-numeric characters.
To represent alphabets in BCD, a 6-bit coding system was developed which could represent numbers, letters and
some special characters. It contains 2 zone bits and 4 numeric bits and can be represented using Octal equivalents.
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