Explain Tabulation Method for simplifying k maps?

The Tabulation Method (QUINE-McCLUSKEY MINIMIZATION)

• An expression is represented in the canonical SOP form if not already in that form.
• A function is converted into numeric notation.
• The numbers can be converted into binary form.
• The minterms can be arranged in a column divided into groups.
• Start with the minimization procedure.
  1. Every minterm of one group is compared with the each minterm in the group immediately below.
  2. Every time a number is found in one group which is the same as a number in the group below except for one digit, the pair numbers is ticked and a new composite is created.
  3. This composite number has the same number of digits as the numbers in the pair except the digit different which are replace by an "x".
• The above process is repeated on second column to generate a third column.
• The next step is to identify the necessarily prime implicants which can be done using a prime implicant chart.
  1. Where the prime implicant covers a minterm the intersection of the corresponding row and column is marked with a cross.
  2. Those columns with only one cross identify the necessary prime implicants these prime implicants must be in the final answer.
  3. The single crosses on the column are circled and all the crosses on the same row are as well circled, indicating that these crosses are covered by the prime implicants selected.
  4. Once one cross on the column is circled all the crosses on that column can be circled since the minterm is now covered.
  5. If any unnecessary prime implicant has all its crosses circled the prime implicant is redundant and need not be considered further.
• After that, selections have to be made from the remaining unnecessary prime implicants, by considering how the crosses not circled can best be covered.
  1. One in common would take those prime implicants which cover the greatest number of crosses on their row.
  2. If all the crosses in the one row as well occur on another row which includes further crosses then the latter is said to dominate the former and can be selected.
  3. The dominated prime implicant can after that be deleted.