BCD Adder

BCD Adder

• The digital systems handle the decimal number in the form of binary coded decimal numbers (BCD). A BCD adder is a circuit that adds two BCD digits and produces a sum digit also in BCD. Here, we will see the implementation of addition of BCD numbers.

• 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 OIIO2 in the sum if sum is greater than 9 or carry is 1.

• The logic circuit to detect sum greater than 9 can be determined by simplifying the boolean expression of given truth table.

• Y = 1 indicates stun is greater than 9. We can put one more term, CQut in the above expression to check whether carry is one. If any one condition is satisfied we add 6 (0110) in the sum.

• With this design information we can draw the block diagram of BCD adder, as shown in the Fig. 3.16.1 (b).

• As shown in the Fig. 3.16.1 (b), the two BCD numbers, together with input carry, are first added in the top 4-bit binary adder to produce a binary sum.

• When the output carry is equal to zero (i.e. when sum ≤ 9 and C_out = 0) nothing (zero) is added to the binary sum. When it is equal to one (i.e. when sum > 9 or C_out = 1), binary 0110 is added to the binary stun through the bottom 4-bit binary adder. The output carry generated from the bottom binary adder can be ignored, since it supplies information already available at the output-carry terminal. 

Ex. 3.16.1 Design an 8-bit BCD adder using 4-bit binary adder.

Sol. : To implement 8-bit BCD adder we have to cascade two 4-bit BCD adders. In cascade connection carry output of the lower position (digit) is connected as a carry input of the higher position (digit). Fig. 3.16.2 shows the block diagram of 8-bit BCD adder.

Ex 3.16.2 Design a BCD to Ex-3 code converter using Binary parallel adder.

Sol.: