Minimum cover for this K-MAP to find minimum SOP; which is better, and why

digital-logickarnaugh map

I used this K-MAP to find the minimum sum-of-products expression for this collection of minterms.

I see that minterm-one could also have been "covered" by grouping it with minterm-five.

I opted to "cover" minterm 1 with the largest possible group: (0,1,2,3), which is the green circle on my K-MAP.

Since both combinations of groups result in a minimum SOP of 5 terms, which would be considered "better" in terms of hardware/gate implementation?

Am I correct to assume that the my larger group is better, as it eliminates one more literal?

Or am I wrong, and would group (1,5) be better than group (0,1,2,3) for finding a minimum SOP?

Karnaugh Map

Best Answer

For hardware implementations, your version with the larger groupings is better. Even though you'll still have five terms, your terms will be more easily implemented since they won't depend on rarely used specific cases.

Think of it like this, if you have a simple AND gate, a larger group reduces the amount of inputs the AND gate will take since its output will be predictable regardless of what any other possible inputs would be. A smaller group makes your AND gate take in more inputs and thus is more complex. You may need more NOT gates before inputting the signal to the AND gate.

Let me know if that is a little confusing.

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