Components required:

Inputs, outputs, NOT gates, AND gates, OR gates, wires.

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Theory:

Minterm-

A minterm is a Boolean expression resulting in 1 for the output of a single cell, and 0s for all other

cells in a Karnaugh map, or truth table. If a minterm has a single 1 and the remaining cells as 0s, it

would appear to cover a minimum area of 1s. It is an expression consisting of all the input terms in

the truth table (in product form), for which the output is 1.

For example, a3.a2.a1.a0 may be minterm but not a3.a1.a0 as it doesn’t contain all the input.

After taking the minterms for all prime nos. between 0-15 the expression we get is:

a3’.a2’.a1.a0 + a3’.a2.a1’.a0 + a3’.a2.a1.a0 +a3.a2’.a1.a0 + a3.a2.a1’.a0

Now we will simplify this expression using K-maps or Boolean algebra.

Procedure:

⮚ Take 4 inputs for the 4 bit number.

⮚ Then take the gates as required to satisfy the expression.

⮚ Connect the gates according to the expression.

⮚ Now Monitor the output at the LEDs for different inputs.

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Truth table:

Decimal A3 A2 A1 A0 p

               0  0   0   0    0

               1  0   0   0     1

2 0 0 1 0

3 0 0 1 1 1

4 0 1 0 0

5 0 1 0 1 1

6 0 1 1 0

7 0 1 1 1 1

8 1 0 0 0

9 1 0 0 1

10 1 0 1 0

11 1 0 1 1 1

12 1 1 0 0

13 1 1 0 1 1

14 1 1 1 0

15 1 1 1 1

Result:

Thus, we realize a circuit to display Prime and Non-Prime numbers (4-bit).