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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

Prime Implicants discussion with help of Karnaugh map (K-map)

What do you mean by prime Implicants?

Final product term obtained from K-map after combining all possible adjacent squares is known as Prime Implicant.  

What are Essential Terms ?

When one Minterm can only be represented by one Prime Implicant then it is called essential term. 

Why it is required ?

It helps in determining other possible simplifications for functions with multiple variables.

Can you explain it with a example?

Yes, check below

Example :-   Consider a function F (x, y, z, w) of 11 Minterms shown in Truth Table

Truth Table

K-map location number
x
y
z
w
Output Function
0
0
0
0
0
1
0
0
0
1
x’y’z’w
2
0
0
1
0
x’y’zw’
3
0
0
1
1
4
0
1
0
0
5
0
1
0
1
x’yz’w
6
0
1
1
0
x’yzw’
7
0
1
1
1
x’yzw
8
1
0
0
0
xy’z’w’
9
1
0
0
1
xy’z’w
10
1
0
1
0
xy’zw’
11
1
0
1
1
12
1
1
0
0
xyz’w’
13
1
1
0
1
xyz’w
14
1
1
1
0
xyzw’
15
1
1
1
1
xyzw