# 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.)

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...

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