A parity circuit determines the parity of a 3-bit input x, y, andz. Odd parity m

Question

A parity circuit determines the parity of a 3-bit input x, y, andz. Odd parity means
there is an odd number of 1s in the 3-bit input (x,y,z), and evenparity means there is an
even number of 1s in the 3-bit input (x,y,z).

Design a parity circuit that outputs 1 if the 3-bit input (x,y,z)contains an even number of 1s.

Express the parity logic function in a truth table. Express it incanonical SOP form.

Using boolean algebra theorems, simplify the logic function so thatit uses a minimum
number of gates.

Explanation / Answer

Truth table Inputs       Output x   y   z      P 0   0   0      0 0   0   1      0 0   1   0      0 0   1   1      1 1   0   0      0 1   0   1      1 1   1   0      1 1   1   1      0 The canonical SOP expression for the output is P = (3,5,6) P = x'yz + xy'z + xyz' P = z(x'y + xy') + xyz' P = z [x XOR y ] + xyz' P = z(x'y + xy') + xyz' P = z [x XOR y ] + xyz'

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