Combinational Circuits

Question 21

Consider the two cascaded 2-to-1 multiplexers as shown in the figure. The minimal sum of products form of the output X is

• A
• B
• C
• D

Question 22

Consider a carry lookahead adder for adding two n-bit integers, built using gates of fan-in at most two. The time to perform addition using this adder is

• Θ(1)
• Θ(Log (n))
• Θ(√ n)
• Θ(n)

Question 23

Consider an eight-bit ripple-carry adder for computing the sum of A and B, where A and B are integers represented in 2’s complement form. If the decimal value of A is one, the decimal value of B that leads to the longest latency for the sum to stabilize is _____________ [This Question was originally a Fill-in-the-blanks Question]

• -1
• 2
• 1
• -2

Question 24

The following circuit implements a two-input AND gate using two 2-1 multiplexers. What are the values of X₁, X₂, X₃ ?

• X₁=b, X₂=0, X₃=a
• X₁=b, X₂=1, X₃=b
• X₁=a, X₂=b, X₃=1
• X₁=a, X₂=0, X₃=b

Question 25

What Boolean function does the circuit below realize ?

• xz+x\'z\'
• xz\'+x\'z
• x\'y\'+yz
• xy+y\'z\'

Question 26

The complement of the function F = (A + B’)(C’ + D)(B’ + C) is:

• A’B + CD’ + BC’
• AB’ + C’D + B’C
• AB’ + CD’ + BC
• AB + BC + CD

Question 27

The number of fill and half-address required to add 16-bit number is:

• 8 half-adders, 8 full-adders
• 1 half-adder, 15 full-adders
• 16 half-adders, 0 full-adders
• 4 half-adders, 12 full-adders

Question 28

A multiplexer with a 4-bit data select input is a

• 4:1 multiplexor

• 2:1 multiplexor

• 16:1 multiplexor

• 8:1 multiplexor

Question 29

The threshold level for logic 1 in the TTL family is

• any voltage above 2.5 V
• any voltage between 0.8 V and 5.0 V
• any voltage below 5.0 V
• any voltage below Vcc but above 2.8 V

Question 30

An N-bit carry look ahead adder, where N is a multiple of 4, employs ICs 74181 (4 bit ALU) and 74182 (4 bit carry look ahead generator). The minimum addition time using the best architecture for this adder is

• proportional to N
• proportional to logN
• a constant
• none of the above