can anyone plz solve this truth table for me. i shall be thank ful to you.

Question:

Prove right hand side equal to left hand site by using truth table

NOTE: Fill the given table and make sure the sequence of input remains same as it is given in the table below.

1. A XOR B = AB’ + A’B

A B A XOR B AB’ A’B AB’ + A’B
0 0
0 1
1 0
1 1

2. BC’ = ABC’ + A’BC’

A B C BC’ ABC’ A’BC’ ABC’+A’BC’
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

3
Contributors
2
Replies
3
Views
8 Years
Discussion Span
Last Post by laehc

I'm guessing you are either struggling with the basics or not bothering to do the work.
I'm only answering 1. A XOR B = AB' + A'B

A B  A XOR B  AB'  A'B  AB'+A'B
0 0     0      0    0      0
0 1     1      0    1      1
1 0     0      1    0      1
1 1     0      0    0      0

Here's an explanation of the second line.
A B
0 1
means "when A is 0 and B is 1" or equivalently "If A is False and B is True".
XOR stands for Exclusive-Or, meaning it's 1 when A or B is 1 but not both of them 1. So when A is 0 and B is 1, A XOR B is one.
AB' stands for A AND (NOT(B)). Because in line 2 B is 1, NOT(B) is 0, so A AND (NOT(B)) is the same as A AND 0. AND only gives a 1 if both things going in are 1, so A AND 0 must give 0.
A'B is 1 because A' is 1 and B is 1.
AB'+A'B is 0+1
In this context + stands for OR which gives 1 if either input is 1.
So 0+1 produces 1, which is the same as A XOR B.
Because the entire column for A XOR B is the same as AB'+A'B, and the table covers all four possible combinations of A with B, A XOR B = AB'+A'B.

Please read that until you understand it, and apply the same reasoning to the other 3 lines, than do the other questions yourself. Hope I haven't made too many mistakes or get told off for helping homework dodgers.

This topic has been dead for over six months. Start a new discussion instead.
Have something to contribute to this discussion? Please be thoughtful, detailed and courteous, and be sure to adhere to our posting rules.