PARITY GENERATOR (3-bit MESSAGE):

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