# Simplify the following Boolean function , using three- variable maps:a) F(x,y,z) = Σ (0,2,6,7)b) F(A,B,C ) = Σ (0,2,3,4,6)c) F(a,b,c) = Σ (0,1,2,3,7)d) F(x,y,z) = Σ (3,5,6,7)

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Simplify the following Boolean function , using three- variable maps:

a) F(x,y,z) = Σ (0,2,6,7)

b) F(A,B,C ) = Σ (0,2,3,4,6)

c) F(a,b,c) = Σ (0,1,2,3,7)

d) F(x,y,z) = Σ (3,5,6,7)

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Step 1

Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like to answer.

Simplify the given Boolean function, using three- variable maps.

The boolean expression needs to simplify in order to reduce its complexity. The highest possible level of complexity is accomplished by the map.

The three-variable map is

Step 2

a) F(x,y,z) = Σ (0,2,6,7)

Consider the minterms, 0, 2, 6, 7. The map for the minterms is

Step 3

The first pattern is X’Y’Z’ and X’YZ’. The simple equation for this pattern is X’Z’.

The second pattern is XYZ and XYZ’. The simple equation for this pattern is XY.

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