Design of Binary to BCD Code Converter Circuit

In this topic, you study how to design Binary to BCD Code Converter Circuit and draw the logic diagram.

Truth table

The input is a 4-bit binary code (A B C D) so 16 (${2^4}$) combinations are possible. Hence the output should have 8-bit, but first three bits will all be a 0 for all combinations of inputs, the output can be treated as 5-bit BCD code (W X Y Z E). The conversion of binary code into BCD code as shown in

truth table 1,

Table 1: Binary to BCD Code Code Converter.

Drawing of K-map for each output

From this truth table, the K-maps are drawing shown in Figure 1, to obtain a minimized expression for each output.

(a) k-map for W

(b) k-map for X

(c) k-map for Y

(d) k-map for Z

(e) k-map for E

Figure 1: k-maps for Binary to BCD Code Converter.

Minimized Expression for each output

The minimized expression for each output obtained from the K-map are given below as

$W = AB + AC$

$X = A \bar B \bar C $

$Y = \bar A B + B C $

$Z = AB \bar C + \bar A C $

$E = D $

Logic Circuit Diagram

Based on the above given minimized expression for each output, a logic circuit can be drawn as shown in Figure 2.

Figure 2: Binary to BCD Code Converter logic diagram.