**Q-Implement the parity generator (a) Even (b) Odd for 3-bit message**

Ans: (a) Following is the truth table and K-map for even parity

a b c P(even)

0 0 0 0

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

1 1 1 1

K-MAP:

Hence the equation we get is P (even) = x xor y xor z

OR P (even) = x xnor y xnor z

(b) Following is the truth table and K-map for odd parity

a b c P(odd)

0 0 0 1

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

K-MAP:

Hence the equation we get is P (odd) = x xnor y xor z = x xor y xnor z = (x xor y xor z)’ = (x xnor y xnor z)’

Hence we see that equations for Parity change with odd or even number of variables

**For odd number of variables**

P (even parity) = x xor y xor z = x xnor y xnor z

P (odd parity) = x xnor y xor z = x xor y xnor z = (x xor y xor z)’ = (x xnor y xnor z)’

**For even number of variables**

P (even parity) = x xor y xor z xor w

P (odd parity) = x xnor y xnor z xnor w

We can similarly implement the following by writing their TRUTH TABLES and drawing their K-MAPS like

(a) Conversion of binary to Excess-3

(b) Conversion of binary to BCD