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written 2.4 years ago by |

**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.