Question
Asked Nov 13, 2019
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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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Expert Answer

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

help_outline

Image Transcriptionclose

Y YZ х 00 01 11 10 X'YZ Х'ҮZ 0 X'Y'Z X'YZ 0 1 2 XYZ 6 XҮ'Z 1 ΧYΖ ХYZ х 4 7

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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

help_outline

Image Transcriptionclose

Y YZ х 00 01 11 10 0 1 1 1 1 х 1

fullscreen
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.

Hen...

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Engineering

Computer Science

Boolean Logic

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