Looping on a K-map always results in the elimination of __________a)Va...
Looping on a K-map always results in the elimination of variables within the loop that appear in both complemented and uncomplemented form.
Looping on a K-map always results in the elimination of __________a)Va...
Variables within the loop that appear in both complemented and uncomplemented form are eliminated when looping on a K-map.
Explanation:
- A Karnaugh map (K-map) is a graphical representation of a truth table that helps simplify Boolean expressions and minimize logic circuits. It consists of cells arranged in a grid, with each cell corresponding to a unique combination of input variables.
- The cells in the K-map are grouped into rectangular regions called loops, which represent the terms in the simplified Boolean expression.
- When looping on a K-map, the goal is to identify adjacent cells that can be combined to form a loop. This is done by grouping cells that have the same output value (0 or 1) and differ by only one input variable.
- While looping, it is important to consider the complemented and uncomplemented forms of the variables within the loop.
- If a variable appears in both its complemented and uncomplemented forms within the loop, it can be eliminated. This is because the variable will always be true or false within the loop, regardless of its input value.
- When a variable appears only in its complemented form within the loop, it cannot be eliminated. This is because its value may change depending on the input combinations outside the loop.
- Similarly, when a variable appears only in its uncomplemented form within the loop, it cannot be eliminated. Its value may also change depending on the input combinations outside the loop.
- Therefore, the variables within the loop that appear in both complemented and uncomplemented form are the ones that can be eliminated when looping on a K-map.
- Eliminating these variables helps simplify the Boolean expression and reduce the number of terms in the final expression, resulting in a more efficient logic circuit design.