Question

1.) Simplify (A xor B) + (A xor C) using k-maps, does (A xor B) + (B xor C) have the same k-map.

Answer 1

Note

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A xor B is 1 if A and B mismatches ie when (A=0 & B=1 ) or when (A=1 & B=0)

Case 1

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For (A xor B) + (A xor C)

When

A=0,B=0,C=0         => (A xor B) + (A xor C) =0+0 =0

A=0,B=0,C=1         =>   0 +1 =1

A=0,B=1,C=0         => 1+ 0 =1

A=0,B=1,C=1         =>   1+1=1

A=1,B=0,C=0         =>   1+1=1

A=1,B=0,C=1         =>   1+0=1

A=1,B=1,C=0         =>    0+1=1

A=1,B=1,C=1         =>   0+0 =0

K Map is as follows

Here we get 3 groups

So the final simplified SOP is

Case 2

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For (A xor B) + (B xor C)

When

A=0,B=0,C=0         => (A xor B) + (B xor C) =0 +0=0

A=0,B=0,C=1         => 0+1=1

A=0,B=1,C=0         => 1+1=1

A=0,B=1,C=1         => 1+0 =1

A=1,B=0,C=0         => 1+0=1

A=1,B=0,C=1         => 1+1=1

A=1,B=1,C=0         => 0+1=1

A=1,B=1,C=1         => 0+0=0

So the K Map for (A xor B) + (B xor C) is as follows

Both (A xor B) + (B xor C) and (A xor B) + (A xor C) have same K Map