Design of BCD to Excess-3 Code Converter Circuit

In this topic, you study how to design BCD to Excess-3 Code Converter Circuit and draw the logic diagram.


Truth table

The BCD (binary coded decimal) code is basically 8421 code and the conversion of 4-bit input BCD code (A B C D) into the excess-3 code output (W X Y Z) as shown in truth table 1.

BCD Code (Input)  Excess-3 Code (Output)
A B C D W X Y Z
0 0 0 0 0 0 1 1
0 0 0 1 0 1 0 0
0 0 1 0 0 1 0 1
0 0 1 1 0 1 1 0
0 1 0 0 0 1 1 1
0 1 0 1 1 0 0 0
0 1 1 0 1 0 0 1
0 1 1 1 1 0 1 0
1 0 0 0 1 0 1 1
1 0 0 1 1 1 0 0
1 0 1 0 X X X X
1 0 1 1 X X X X
1 1 0 0 X X X X
1 1 0 1 X X X X
1 1 1 0 X X X X
1 1 1 1 X X X X

Table 1: BCD to Excess-3 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.

BCD to Excess-3 Code Converter k-map 1

(a) k-map for W

BCD to Excess-3 Code Converter Circuit

(b) k-map for X

BCD to Excess-3 Code Converter k-map 3

(c) k-map for Y

BCD to Excess-3 Code Converter k-map 4

(d) k-map for Z

Figure 1: k-maps for BCD to Excess-3 Code Converter.

Minimized Expression for each output

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

$W = A + BC + BD$

$X = \bar B C + \bar B D + B\bar C \bar D $

$Y = CD + \bar C \bar D $

$Z = \bar 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.

BCD to Excess-3 Code Converter logic diagram

Figure 2: BCD to Excess-3 Code Converter logic diagram.

Published by

Electrical Workbook

We provide tutoring in Electrical Engineering.

Leave a Reply

Your email address will not be published. Required fields are marked *