BCD Addition

BCD numbers are numerical numbers. So, arithmetic operations can be performed on BCD numbers. Imagine a seven-segment timer display system showing 2 digits for the count of seconds. After every second, the timer should be incremented by 1. This means that the timer display system requires a BCD adder at the backend, whose output is shown on display.

So, let’s learn how to add two BCD numbers. Though BCD addition follows the rules of binary arithmetic, there are some additional things that need to be taken care of.

Steps of BCD Addition

Step 1: Add the two BCD numbers using the rules for binary addition. Step 2: If a 4-bit sum is equal to or less than 9, it is a valid BCD number. Step 3: If a 4-bit sum is greater than 9 or if a carry-out of the 4-bit group is generated, it is an invalid result. Add 6 (0110) to the 4-bit sum in order to skip the six invalid BCD code words and return the code to 8421. If a carry results when 6 is added, simply add the carry to the next 4-bit group.

Example 1: Find the sum of the BCD numbers 01000011 + 00110101

Solution:

Decimal number of the given BCD numbers are as below:

01000011_BCD = 43₁₀ and 00110101_BCD = 35₁₀

In the above example, all the 4-bit BCD additions generate valid BCD numbers, which means less than 9. So, the final correct result is 78₁₀ = 01111000_BCD.

Let’s take an example where the addition generates an invalid BCD number.

Example 2: Find the sum of the BCD numbers 01110101 + 00110101

Solution:

The decimal number of the given BCD numbers are as below:

01110101_BCD = 75₁₀ and 00110101_BCD = 35₁₀

 

In the above example, both the BCD code addition generated result larger than 9, so invalid. To get the correct result, we added 6 (0110₂) to both the invalid sum. Notice that the carry generated from the left group is forwarded to the right group. The final correct result is 110₁₀ = 000100010000_BCD.

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