Solution:

Mapping a Standard SOP Expression:

• For an SOP expression in standard form, a 1 is placed on the Karnaugh map for each product term in the expression.

• Each 1 is placed in a cell corresponding to the value of a product term.

• For example, for the product term ABC, a 1 goes in the 101 cell on a 3-variable map.

• When an SOP expression is completely mapped, there will be a number of 1s on the Karnaugh map equal to the number of product terms in the standard SOP expression.

• The cells that do not have a 1 are the cells for which the expression is 0. Usually, when working with SOP expressions, the 0s are left off the map.

• The following steps and the illustration in Figure show the mapping process.

  • Step 1: Determine the binary value of each product term in the standard SOP expression. After some practice, you can usually do the evaluation of terms mentally.

  • Step 2: As each product term is evaluated, place a 1 on the Karnaugh map in the cell having the same value as the product term.

Mapping a Standard POS Expression:

• For a POS expression in standard form, a 0 is placed on the Karnaugh map for each sum term in the expression.

• Each 0 is placed in a cell corresponding to the value of a sum term.

• For example, for the sum term A + B + C, a 0 goes in the 010 cell on a 3-variable map.

• When a POS expression is completely mapped, there will be a number of 0s on the Karnaugh map equal to the number of sum terms in the standard POS expression.

• The cells that do not have a 0 are the cells for which the expression is 1.

• Usually, when working with POS expressions, the 1s are left off.

• The following steps and the illustration in Figure show the mapping process.

  • Step 1: Determine the binary value of each sum term in the standard POS expression. This is the binary value that makes the term equal to 0.

  • Step 2: As each sum term is evaluated, place a 0 on the Karnaugh map in the corresponding cell.