BCD Adder, Mux (Multiplexer) & DeMux(Demultiplexer)

BCD stand for binary coded decimal. Suppose, we have two 4-bit numbers A and B. The value of A and B can varies from 0(0000 in binary) to 9(1001 in binary) because we are considering decimal numbers.

BCD or Binary Coded Decimal is that number system or code which represents the 10 decimal digits in terms of binary numbers.

The following is table for Decimal number and it’s Binary Equivalent:

As seen above, when the Decimal equivalent exceeds 9, then we start writing the BCD equivalent as two Binary equivalents.

Now let’s have a look at some examples:

0101 + 0011 = 1000 (Binary addition). [If you compare this with the above table, you’ll find that 0101 is 5; 0011 is 3 and 1000 is 8.] We can do the same for every number whose sum comes to less than or equal to 9.

But if the addition is greater than 9,then what!

Simple! Let’s take an example:

0101 + 1000 = 1101 . [From table, 0101 is 5; 1000 is 8 and 1101 is 13.]

But the BCD equivalent of 13 is 0001 0011.

So we take the Binary addition obtained i.e 1101 and add 0110 (decimal 6) to it.

The result obtained is 1101 + 0110 = 1 0011 where the last 4 bits 0011 represent 3and 1(can also be written as 0001, which means 1 in decimal equivalent). Thus we obtain 0001 0011 as final answer!

Thus, for any addition greater than 9, add binary equivalent of 6 to the Binary sum obtained and you’ll get it’s BCD equivalent.

1. Add two BCD numbers using ordina7 binary addition. 
2. If four-bit sum is equal to or less than 9, no correction is needed. The sum is in proper BCD form.
3.  If the four-bit sum is greater than 9 or if a carry is generated from the four-bit sum, the sum is invalid. To correct the invalid sum, add 0110 to the four-bit sum.
4.  If a carry results from this addition, add it to the next higher-order BCD digit. 
5. Thus to implement BCD adder we require : 4-bit binary adder for initial addition Logic circuit to detect sum greater than 9 and One more 4-bit adder to add 0110 in the sum if sum is greater than 9 or carry is 1.

For BCD Adder - Click here

For Multiplexer and Demultiplexer - Click here