Question 7.16: Given a 3-variable function g(C,B,A) = ∑(2,3,4,5), find a ma...
Given a 3-variable function g( C,B,A ) = ∑( 2,3,4,5), find a maximally simplified SOP form using K. maps. Figure 7.8 depicts function g minterms on a 3-variable K. map.
Let us begin by encircling the largest possible number of adjacent minterms, such that that number is a power of two. We clearly obtain one grouping with minterms m_2 and m_3 and a second and last grouping produces the grouping of m_4 and m_5. The solution to this problem is particularly straightforward because we do not have other choices of encircling minterms that would produce similar results. Referring to Figure 7.8 we see that the maximally simplified SOP form yields:
g(C,B,A)=\sum{(2,3,4,5,)}=C\bar{B} +\bar{C}B
Note: The solution of Example 7.16 is the exclusive or of which variables? Answer: B, C.