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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.

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