Truth table

The conversion of 4-bit input Gray code (A B C D) into the Binary code output (W X Y Z) as shown in truth table 1. The 4-bit input so 16 (${2^4}$) combinations are possible and all of them are valid so no don’t care condition.

Table 1: Gray to Binary 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

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

Minimized Expression for each output

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

$W = A$

$X = \bar A B + A \bar B = A \oplus B $

$Y=\bar{A}\bar{B}C+\bar{A}B\bar{C}+ABC$

$+A\bar{B}\bar{C}$

$=A\oplus B\oplus C$

$Y = X \oplus C$

$Z = \bar A\bar B\bar CD + \bar A\bar BC\bar D + \bar AB\bar C\bar D $

$+\bar{A}BCD\text{ }\!\!~\!\!\text{ }+AB\bar{C}D+ABC\bar{D}$

$+A\bar{B}\bar{C}\bar{D}+A\bar{B}CD$

$Z=A\oplus B\oplus C\oplus D$

$Z = Y \oplus D$

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: Gray to Binary Code Converter logic diagram.

The post Design of Gray to Binary Code Converter Circuit appeared first on ElectricalWorkbook.

Truth table

The conversion of 4-bit input Binary code (A B C D) into the Gray code output (W X Y Z) as shown in truth table 1. The 4-bit input so 16 (${2^4}$) combinations are possible and all of them are valid so no don’t care condition.

Table 1: Binary to Gray 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

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

Minimized Expression for each output

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

$W = A$

$X = \bar A B + A \bar B = A \oplus B $

$Y = \bar B C + B \bar C = B \oplus C $

$Z = \bar C D  + C \bar D = C \oplus 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 Gray Code Converter logic diagram.

The post Design of Binary to Gray Code Converter Circuit appeared first on ElectricalWorkbook.

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.

The post Design of Binary to BCD Code Converter Circuit appeared first on ElectricalWorkbook.

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.

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.

The post Design of BCD to Excess-3 Code Converter Circuit appeared first on ElectricalWorkbook.