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BCD addition and Decimal Arithmetic

Refer complete digital basics tutorial

 

In BCD addition of two numbers involve following rules:-

1. Maximum value of the sum for two digits = 9 (max digit 1) + 9 (max digit 2) + 1 (previous addition carry) = 19

2. If sum of two BCD digits is less than or equal to 9 (1001) without carry then the result is a correct BCD number.

3. If sum of two BCD digits is greater than or equal to 10 (1010) the result is in-correct  BCD number. Perform steps 4 for correct BCD sum.

4. Add 6 (0110) to the result.

Examples:- BCD Addition

Add 599 and 984 using BCD numbers

Answer.  Result of BCD addition is 1583

Nice plot for above calculations below:

Binary Sum 1, 2 and 3 are greater than 1010.

So, from Step 3 and 4 add ‘6’ to the sum.

BCD Coding and addition examples

Introduction to BCD :-

> BCD stands for Binary Encoded Digital. In BCD every decimal number is represented by four binary bits.

 

> 190 in decimal is equivalent to 0001 1001 0000 in binary encoded decimal

> 0 to 9 in decimal can be represented in binary using four digits and all integers can be represented by these 10 digits.

8
5
3
1
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BCD
1
2
3
599
0101
1001
1001
+984
1001
1000
0100
SUM
1110
10001
1101
carry 1
carry 1
carry 1
Result
1110
10001
1101
+6
0110
0110
0110
End carry 1
0101(5)
1000 (8)
0011 (3)
Gray Coding.Digital gates.
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