# Need help on combinational circuit design

#### cat

Joined Sep 25, 2006
8
Hello

There are 3 inputs x,y,z and three outputs A,B,C
when the binary input is 0,1,2,3, output is one grater than the input
when the binary input is 4,5,6,7, output is one less than the input.

I came up with this truth table but i don't know whether this is the correct way or not

x y z A B C
0 0 0 0 0 1
0 0 1 0 1 0
0 1 0 0 1 1
0 1 1 1 0 0
1 0 0 0 1 1
1 0 1 1 0 0
1 1 0 1 0 1
1 1 1 1 1 0

according to this
A=xy+yz+xz
B=x'y'z+x'yz+xy'z+xyz
C=z'

any reply would be greatly appreciated
thanks
cat

#### thingmaker3

Joined May 16, 2005
5,083
Table is correct. Equations for A and for C are correct.

#### Dave

Joined Nov 17, 2003
6,969
From your truth table I get the following equation for B:

B = x'y'z + x'yz' + xy'z' + xyz

Which simplifies to:

B = x'(y'z + yz') + x(y'z' + yz)

There are many simplifications for B, depending on what you take as the common factor, i.e. you could easily have taken y and y', or z and z' as common factors to simplify B. This is highly dependant on how you wish to represent your variables.

Dave