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:
- Preparing index value based on number of 1’s in the minterms of the equation including don’t care terms.
- Rearranging the minterms as per index value
- Checking minterms from one group to another for a 1-bit change and ticking such terms.
- Repeating step-3 till such time no further pairing of minterms are possible. All such terms are called as prime implicants terms
- Preparing PI chart to find essential prime implicants
Simplify Y(A,B,C,D) = ∑m(0,2,3,6,7,8,10,12,13) using McClusky or the Tabulation method
Step-1: Prepare index value (i.e. find number of 1’s in each minterm)
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’
Solve the following Boolean expressions using Tabulation method
- Y(A,B,C,D) = ∑m(0,1,2,5,6,7,8,9,10,14)
- Y(A,B,C,D) = ∑m(0,5,8,9,10,11,14, 15)
- Y(A,B,C,D) = ∑m(0,1,3,7,8,9,11,15)
- Y(A,B,C,D) = ∑m(4,6,9,10,11,13) + ∑d(2,12,15)