Answer to Question #192636 in Electric Circuits for Jane

Question

Q2. Design a combinational circuit with four inputs, w, x , y , and z , and four outputs, A, B , C and D. When the binary input is 0, 1, 2, or 3, the binary output is two greater than the input. When the binary input is 4, 5, 6, or 7, the binary output is one less than the input. Solve with four inputs and outputs.

Answer 1

Step1:. Derive the truth table that defines the required relationship between inputs and outputs.

Step2: Obtain the simplified Boolean functions for each output as a function of the input variables. 

Map For output A:

The simplified expression from the map is: $A = w$

Map for output B:

The simplified expression from the map is:  $\boxed{B=w'y+xz+wx}$

Map for output C:

The simplified expression from the map is:$\boxed{C=w'x'y'+w'y'z'+xyz+wy}$

Map for output D:

The simplified expression from the map is:$\boxed{D=x'z+w'xz'+wz}$

Step3. Draw the logic diagram.

$A=w$

$B = w'y+xz+wx$

$C = w'x'y'+w'y'z'+xyz+wy$

$D = x'z+w'xz'+wz$