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PLEASE EXPLAIN ALL STEPS (including how k-map formation is formed): simplify the boolean equations: xz + (xy + ~z) ~xyz + yz + x~y

Question

PLEASE EXPLAIN ALL STEPS (including how k-map formation is formed):

simplify the boolean equations:

  1. xz + (xy + ~z)
  2. ~xyz + yz + x~y
check_circleAnswer
Step 1

Some of the simple rules follows to simplify Boolean expression:

AND gate rule:
OR gate rule:
Expression Equivalent
value
Expression Equivalent
value
А
A+A
А
А.А
0
A+A
1
A.A
1
A+1
A.1
0
A+0
A
А.О
DeMorgan's Theorem:
Expression
Equivalent value
A+AB
A+B
АВ
AB
А.В
A+B
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AND gate rule: OR gate rule: Expression Equivalent value Expression Equivalent value А A+A А А.А 0 A+A 1 A.A 1 A+1 A.1 0 A+0 A А.О DeMorgan's Theorem: Expression Equivalent value A+AB A+B АВ AB А.В A+B

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Step 2

Simplify the Boolean equations: xz + (xy + ~z)

For simplifying the Boolean expression, use Karnaugh Map and follow the below steps-

  1. a) Fill 1 at decimal equivalent number 0,2,5,6,7 as per the given question accordingly in the K-map.
  2. b) Then pairing will be done in the K-map.

c)There will be three pairs formed in this K -map as shown below –

 

 

 

_
yz
УZ
УZ
1
1
X
0
1
3
2
X
1
1
7
IN
| N
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_ yz УZ УZ 1 1 X 0 1 3 2 X 1 1 7 IN | N

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Step 3

The final expression i...

XZ XZ XY
(X OZ)XY
1t Pair XZ
2nd Pair XZ
3rd Pair XY
(XO Z)+XY
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XZ XZ XY (X OZ)XY 1t Pair XZ 2nd Pair XZ 3rd Pair XY (XO Z)+XY

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