XOR operations. You remember operation with A B = AB\' + BA\'. You remember the

Question

XOR operations. You remember operation with A B = AB' + BA'. You remember the commutative law, associative law and also Interesting things about A 0, A I, A A, A A', A B = A C implies B = C, and the application to WiFi. (a) Prove or disprove if A B = C, then A C = B. (b) Prove or disprove if A B = C D, then A C = B D. Here A, B, C, D are all signals of 1 bit equal to 0 or 1. FYI: Try your best to solve as many questions as possible. Grading will be done by curve and top few will get A and A. Try to make sure your accumulated score is at least 40 points for passing.

Explanation / Answer

Given;
a)
AB = C====>(1)

We need to Prove AC = B===>(2)

Lets start with LHS

AC => We know that AB = C So replace C by AB
=> AAB ==>We know that AA = 0
=> 0B ==>We know that 0B = B
=> B

Hence Proved AC = B
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b)

Given;
AB = CD====>(1)

We need to Prove AC = BD===>(2)

Lets start with the second equation

AC = BD => Apply A on both the sides i.e LHS and RHS
=> AAC = ABD ==>We know that AA = 0
=> C = ABD ==>We know that AB = CD Given
=> C = CD D ==>We know that dD = 0
=> C = C0
=> C = C
Hence Proved AC = BD


Thanks, let me know if there is any concern.


Hence Proved AC = B

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