Given the following Karnaugh Map for a Boolean function 𝐹(𝑤, 𝑥, 𝑦, 𝑧):…

Step 1: Find groups of 1s on the Karnaugh map and identify common variables.

• Group of four covering cells where x = 0 and z = 0 (w and y vary): these four minterms are \bar{w}\bar{x}\bar{y}\bar{z}, w\bar{x}\bar{y}\bar{z}, \bar{w}\bar{x}y\bar{z}, w\bar{x}y\bar{z} which simplify to \bar{x}\bar{z}.

• Group of four covering cells where x = 1 and z = 1 (w and y vary): these minterms combine to x z.

Step 2: Write the simplified function by OR-ing the group results.

F(w,x,y,z) = \bar{x}\bar{z} + x z

Note: The expanded expression \bar{w}\bar{x}\bar{y}\bar{z} + w\bar{x}\bar{y}\bar{z} + \bar{w}\bar{x}y\bar{z} + w\bar{x}y\bar{z} + x z is algebraically equivalent to \bar{x}\bar{z} + x z because the four minterms shown collapse to \bar{x}\bar{z}.

Tip: To check any proposed expression, expand it into minterms and verify each minterm against the 1-cells of the K-map; any minterm present in the expression must correspond to a 1-cell, and every 1-cell must be covered by at least one term.