Logic Circuits: 3-bit K-Map (Karnaugh Map) problem #2

Solution:
This is a summation of minterms, therefore, 0, 2, 3, and 7 are all 1's. We can't group the 4 of them together since they don't form a square in the K-map (see figure). We can group them by pair. Notice the ones grouped in red. They can be grouped together since the difference between bits 00 and 10 is only 1 bit, and we can only group together bits that are 1 bit apart (review Gray Code, K-map is in Gray Code). When dealing with minterms, an x is equal to 1 and an x' is equal to 0. Zero's will be listed as x' and one's as x.

We need to list the variables. For the first term (red group), A has two 0's, B has one 0 and one 1, and C has two 0's. For the second term (green group), A has one 0 and one 1, B has two 1's, and C has two 1's as well.