## Monday, April 4, 2011

### IMPLEMENTATION OF BOOLEAN FUNCTIONS

IMPLEMENTATION OF BOOLEAN FUNCTIONS

AIM:

To design the logic circuit and verify the truth table of the given Boolean expression,
F (A, B, C, D) = Σ (0, 1, 2, 5, 8, 9, 10)

[Design can be changed by changing the Boolean expression]

APPARATUS REQUIRED:
 S.No Name of the Apparatus Range Quantity 1. Digital IC trainer kit 1 2. AND gate IC 7408 3. OR gate IC 7432 4. NOT gate IC 7404 5. NAND gate IC 7400 6. NOR gate IC 7402 7. EX-OR gate IC 7486 8. Connecting wires As required

DESIGN:

Given ,  F (A,B,C,D) = Σ (0,1,2,5,8,9,10)

The output function F has four input variables hence a four variable Karnaugh Map is used to obtain a simplified expression for the output as shown,

From the K-Map,
F = B’ C’ + D’ B’ + A’ C’ D
Since we are using only two input logic gates the above expression can be re-written as,
F = C’ (B’ + A’ D) + D’ B’
Now the logic circuit for the above equation can be drawn.

CIRCUIT DIAGRAM:

TRUTH TABLE:

 S.No INPUT OUTPUT A B C D F=D’B’+C’(B’+A’D) 1. 0 0 0 0 1 2. 0 0 0 1 1 3. 0 0 1 0 1 4. 0 0 1 1 0 5. 0 1 0 0 0 6. 0 1 0 1 1 7. 0 1 1 0 0 8. 0 1 1 1 0 9. 1 0 0 0 1 10. 1 0 0 1 1 11. 1 0 1 0 1 12. 1 0 1 1 0 13. 1 1 0 0 0 14. 1 1 0 1 0 15. 1 1 1 0 0 16. 1 1 1 1 0

PROCEDURE:

1. Connections are given as per the circuit diagram
2. For all the ICs 7th pin is grounded and 14th pin is given +5 V supply.
3. Apply the inputs and verify the truth table for the given Boolean expression.

RESULT:

The truth table of the given Boolean expression was verified.