﻿ Prime Implicants discussion with help of Karnaugh map (K-map) and examples.
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Prime Implicants discussion with help of Karnaugh map (K-map) - Contd.

Gate level Minimization Example. Refer prime implicants basics from here

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

Truth Table

So Following are the Four Essential Prime Implicants.

z’w, xz’, xw, x’zw’

Next step is to map remaining two(7 and 10)  minterms in all possible combinations.

for Minterm 7,

yw or yz

for Minterm 10,

xy or yz

So the final simplified solutions of the function are

Solution 1.   z’w + xz’+ xw + x’zw’ + yw + xy

Solution 2.   z’w + xz’+ xw + x’zw’ + yz

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

K– map plot of 11 Minterms

There are Four essential terms for the function in discussion. The essential terms are shown within squares in the Truth Table.

zw

xy

Interview Questions. Main, FPGA, Digital Fundamentals
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
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