Combination Circuits

PARITY GENERATOR (4-bit MESSAGE)

Q-Implement the parity generator (a) Even (b) Odd for 4-bit message

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

Binary number                  Parity (even)

0000                                       0

0001                                       1

0010                                       1

0011                                       0

0100                                       1

0101                                       0

0110                                       0

0111                                       1

1000                                       1

1001                                       0

1010                                       0

1011                                       1

1100                                       0

1101                                       1

1110                                       1

1111                                       0

K-MAP for even parity:

We know this is the K-map for XOR gate. Hence the equation we get is P (even) = x xor y xor z xor w

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

Binary number                  Parity (odd)

0000                                       1

0001                                       0

0010                                       0

0011                                       1

0100                                       0

0101                                       1

0110                                       1

0111                                       0

1000                                       0

1001                                       1

1010                                       1

1011                                       0

1100                                       1

1101                                       0

1110                                       0

1111                                       1

K-map for odd parity:

We know this is K-map for XNOR gate. Hence the equation we get is P (odd) = x xnor y xnor z xnor w

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