Mc-Clusky or Tabulation Method

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Introduction

In the previous lectures, you have learnt the Boolean algebra and K-Map methods of solving Boolean expressions.

These methods are simple and easy for less number of variables say upto four. But for more than 4 variable equations, these become tedious. So, another method known as Quine Mc-Clusky or Tabulation Method is used for solving Boolean expression involving four or more variables.

Quine Mc-Clusky or Tabulation Method

This is again a simple method but requires lot of concentration while looking for minterms with 1-bit change. A little distraction of mind will lead to committing a mistake.

Various steps involved in simplification are:

1. Preparing index value based on number of 1’s in the minterms of the equation including don’t care terms.
2. Rearranging the minterms as per index value
3. Checking minterms from one group to another for a 1-bit change and ticking such terms.
4. Repeating step-3 till such time no further pairing of minterms are possible. All such terms are called as prime implicants terms
5. Preparing PI chart to find essential prime implicants

Example:

Simplify Y(A,B,C,D) = ∑m(0,2,3,6,7,8,10,12,13) using McClusky or the Tabulation method

Solution

Step-1: Prepare index value (i.e. find number of 1’s in each minterm)

minterm	mo	M2	M3	M6	M7	M8	M10	M12	M13
Binary	0000	0010	0011	0110	0111	1000	1010	1100	1101
Index	0	1	2	2	3	1	2	2	3

 

Step-2: Group the minterms as per index value

At this point, one can start combining minterms with other minterms. If two terms vary by only a single digit changing, that digit can be replaced with a dash indicating that the digit doesn’t matter. Terms that can’t be combined any more are marked with an asterisk (*)

Step-3: Preparing PI Char for finding Essential Prime Implicants

So, the final solution of the expression Y(A,B,C,D) = ∑m(0,2,3,6,7,8,10,12,13) is:

Y   = A’C   +  B’D’    +  ABC’

 

Exercise:

Solve the following Boolean expressions using Tabulation method

1. Y(A,B,C,D) = ∑m(0,1,2,5,6,7,8,9,10,14)
2. Y(A,B,C,D) = ∑m(0,5,8,9,10,11,14, 15)
3. Y(A,B,C,D) = ∑m(0,1,3,7,8,9,11,15)
4. Y(A,B,C,D) = ∑m(4,6,9,10,11,13) + ∑d(2,12,15)