MadeEasy WorkBook: Digital Logic - Multiplexer

Question

Why In' is taken as A'B'C'D'? 

Comments

A',B',C' and D' are not to be confused with complement of A,B,C and D resp.

Instead they should have written S3,S2,S1,S0.

Since $I_{13}$ comes as the o/p of MUX, so we know that select lines of MUX must have been 1101 i.e. A=1,B=1,C=0,D=1.

Now its given that $I_n$ is the corresponding o/p of DeMux.

Lets check the select lines of DeMux:

S3 = A xor B = 1 xor 1 =0

S2=BD=1.1=1

S1=(D')'=D = 1

S0= C nand A = 0 nand 1 = 1

So select lines of DeMux (S3,S2,S1,S0) is 0111 which selects $I_n$ so it must be $(0111)_2=(7)_{10}$

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OK... Thanks