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.
(a) k-map for W
(b) k-map for X
(c) k-map for Y
(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.
Figure 2: BCD to Excess-3 Code Converter logic diagram.