Handling More Complex Circuits

 


Three Inputs (A, B, C), Three Outputs (D, E, F)

D = ABC + ABC + ABC + ABC + ABC + ABC + ABC
E = ABC + ABC + ABC + ABC + ABC + ABC + ABC
F = ABC + ABC + ABC + ABC + ABC + ABC + ABC


Simplify a little...

(We noticed that E is always 1 when A is 1 (as well as 3 other times) and that F is always 1 when A is 0 (as well as 3 other times.)

'Complex' Circuit Diagram
D = ABC + ABC + ABC
     + ABC + ABC + ABC + ABC
E = A + AB + ABC
F = A + AB + ABC

(We've gone from 24 gates to 12.)


Simplify more using Boolean Algebra...

'Complex' Circuit Diagram
D = A + AB + ABC
E = A + AB + ABC
F = A + AB + ABC

(Now we've gone to 9 gates, but algebraic simplification of boolean expressions isn't always easy.)


Alyce Brady, Kalamazoo College