Asked Oct 5, 2019

Please explain, as simplistically (but thoroughly) as possible, how to develop a k-map from a truth table to be used to simplify an equation.


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

Expert Answer

Step 1

Rules to be followed to simplify the Boolean expression are given below-


Image Transcriptionclose

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

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 –


Image Transcriptionclose

yz УZ Уz X 1 1 X 0 3 X 1 1 4 5 The final expression is shown below- XZXZ+XY (X Z) XY 1S Pair XZ 2nd Pair XZ 3rd Pair XY — (Х®Z)+XY IN I N

Step 3

Now, to find the truth table for the final expression xz + (xy + ~z), firstly calculate the truth tabl...


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