Gray Code Rule & K-Map

Gray Code Rule:

This rule stands for a pair of Binary bits where every successive pair of numbers differs in only 1 bit starting from the rightmost bit.

example:

Input pair     :   00

next             :    01    (only Right bit is changed and Left bit is carry forwarded)

next             :    11    (only Left bit is changed and Right bit is carry forwarded)

next             :    10    (only Right bit is changed and Left bit is carry forwarded)

K-Map:

Also known as Karnaugh Map is a way to simplify Boolean Functions & Expressions.

Any expression reduced using K-Map can not be further reduced.

It is used to reduce 2-bits, 3-bits & 4-bits input boolean functions and expressions.

In this method we create groups by sharing the filled 1's OR 0's to reduce the given functions.

Type of Groups :

There are following type of groups possible depending on number of inputs

a) Hexa (group of 16 1's OR 0's)

b) Octet (group of 8 1's OR 0's)

c) Quad (group of 4 1's OR 0's)

d) Pair (group of 2 1's OR 0's)

e) Singlet (single 1 OR 0)

Rules for Grouping :

Following are the rules for making groups in K-map.

a) This is the first and most important rule that there should be Minimum Number of Groups.

b) Secondly, make Group of Maximum 1's OR 0's by Maximum Sharing.

c) Lastly, Remove Redundant Groups, i.e. remove those groups whose every "1" OR "0" is shared in other groups. It should be ensured that every group should have atleast one "0" OR "1", which is not part of any other group.

Figures Representing Various Groups:

1) Groups can be Horizontal or Vertical, but can't be a Diagonal.

2) Groups must be of 1,2,4,8 or 16 1's OR 0's, i.e. in the form of 2ⁿ

3) Make large groups with maximum sharing.

4) Groups are formed using Map rolling.