Final answer:
When four 1s are grouped together on a Karnaugh map, two variables are eliminated, leading to a simpler Boolean expression. This grouping represents a square on the map, meaning two variables remain constant, and the other two are removed from this part of the expression.
Step-by-step explanation:
When four 1s are grouped together on a Karnaugh map, two variables are eliminated from the output expression. A Karnaugh map is a visual representation used to simplify the Boolean algebra expressions that arise in digital logic circuits. By grouping together adjacent cells that contain the value 1, you can form groups of 1, 2, 4, 8, etc., which correspond to simplifying the expression.
For a group of four 1s, you can eliminate two variables because each dimension of the Karnaugh map represents a binary variable. In a two-dimensional Karnaugh map, a group of four creates a square, indicating that those four 1s have two variables in common that remain unchanged over the group, while the other two variables that change are eliminated from the output expression.
To illustrate with an example, consider variables A, B, C, and D. If we group four 1s together, where A and B hold steady (say both equal to 1), while C and D change across the four cells (from 00 to 11), we can simplify this to just 'A and B' in the Boolean expression, eliminating C and D from this part of the output expression.
Eliminate terms wherever possible is key to simplifying the algebra involved in creating the expression from the Karnaugh map. Upon completing this process, always check the answer to see if it is reasonable and accurately reflects the minimal form.