Consider the 2-bit multiplexer (MUX) shown in the figure. For OUTPUT to be the XOR of C and D, the values for A₀, A₁, A₂, and A₃ are ________.

The correct answer is option 3.

Concept:

The multiplexer abbreviated "MUX" or "MPX," is a combinational logic circuit that uses a control signal to switch one of the numerous input lines to a single common output line.

S${}_{1,}$ S₀ are the select lines, I₁, I₂, I₃, and I₄ are the input lines and produce the output Y.



Y= (S₁' S₀' )I₀+( S₁'S₀)I1+(S₁ S₀' )I2 +( S₁S₀ )I3

Explanation:

Option 1: A 0 = 0, A 1 = 0, A 2 = 1, A 3 = 1

These input lines A 0 = 1, A 1 = 0, A 2 = 1, A 3 = 0, C and D are the select lines and produce the output

Y= (C' D' ) 0 +( C' D ) 0 +(C D' ) 1 +( CD) 1

Y=0+0+CD'+CD

Y=C(D'+D)

Y=C

Option 2: A 0 = 1, A 1 = 0, A 2 = 1, A 3 = 0

These input lines A0 = 0, A1 = 0, A2 = 1, A3 = 1, C and D are the select lines and produce the output

Y= (C'D') 1+( C' D ) 0+(C D' ) 1+( CD) 0

Y= C'D'+0+CD'+0

Y=D'(C'+C)

Y=D'

Option 3: A 0 = 0, A 1 = 1, A 2 = 1, A 3 = 0

These input lines A 0 = 0, A 1 = 1, A 2 = 1, A 3 = 0, C and D are the select lines and produce the output

Y= (C'D') 0+( C' D) 1+(CD') 1+( CD) 0

Y= 0 + C'D + CD' + 0

Y=C'D + CD'

Option 4: A 0 = 1, A 1 = 1, A 2 = 0, A 3 = 0

These input lines A 0 = 1, A 1 = 1, A 2 = 0, A 3 = 0, C and D are the select lines and produce the output

Y= (C'D') 1 + ( C' D ) 1 + (C D' ) 0 + ( CD) 0

Y= C'D '+ C'D + 0 + 0

Y=C'D '+ C'D

Y=C'(D' + D)

Y = C'

Hence the correct answer isA 0 = 0, A 1 = 1, A 2 = 1, A 3 = 0.