Combinational Circuits · Digital Logic · GATE CSE

Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?

Which one of the following circuits implements the Boolean function given below?

f(x, y, z) = m₀ + m₁ + m₃ + m₄ + m₅ + m₆, where m_i is the i^th minterm.

A multiplexer is placed between a group of 32 registers and an accumulator to regulate data movement such that at any given point in time the content of only one register will move to the accumulator. The minimum number of select lines needed for the multiplexer is _____.

If there are m input lines and n output lines for a decoder that is used to uniquely address a byte addressable 1 KB RAM, then the minimum value of m + n is ____.

In the following truth table $$V=1$$ if and only if the input is valid.

What function does the truth table represent?

The Boolean expression for the output $$f$$ of the multiplexer shown below is

How many $$3$$ to $$8$$ decodes with an enable input are needed to construct to constant $$6$$ to $$64$$ line decoder without using any other logic gates

Consider a digital logic circuit consisting of three 2-to-1 multiplexers M1, M2, and M3 as shown below. X1 and X2 are inputs of M1. X3 and X4 are inputs of M2. A, B, and C are select lines of M1, M2, and M3, respectively.

For an instance of inputs X1=1, X2=1, X3=0, and X4=0, the number of combinations of A, B, C that give the output Y=1 is ______________

A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function $$\overline A + \overline A \,.\,\overline C + A\,.\,\overline B \,.\,C$$ ?

Consider the two cascaded $$2$$-to-$$1$$ multiplexers as shown in the figure.

The minimal sum of products form of the output $$X$$ is

Consider the $$4$$-to-$$1$$ multiplexer with two select lines $${S_1}$$ and $${S_0}$$ given below

The minimal sum-of-products form of the Boolean expression for the output $$F$$ of the multiplexer is

Suppose only one multiplexer and one inverter are allowed to be used to implement any Boolean function of $$n$$ variables. What is the minimum size of the multiplexer needed?

Consider the circuit above. Which one of the following options correctly represents $$f(x,y,z)?$$

Consider the $$ALU$$ shown below

If the operands are in $$2's$$ complement representation, which of the following operations can be performed by suitably setting the control lines $$K$$ and $${C_0}$$ only ( + and - denote addition and subtraction respectively)?

Consider the following multiplexer where $$10, 11, 12, 13$$ are four data input lines selected by two address line combinations $${A_1}\,{A_0} = 00,01,10,11$$ respectively and $$f$$ is the output of the multiplex (or). $$EN$$ is the Enable input.

The function $$f(x,y,z)$$ implemented by the above circuit is

Consider the circuit shown below. The output of a $$2:1$$ Mux is given by the function $$(ac+bc)$$

Which of the following is true?

Consider the circuit in fig shown $$f$$ implements

Consider the circuit in Fig. Which has a four bit binary number $${b_3}\,{b_2}\,{b_1}\,{b_0}\,$$ as input and a five bit binary number $${d_3}\,{d_2}\,{d_1}\,{d_0}\,$$ as output. The circuit implements:

Fill in the blanks:
In the two bit full-adder/sub tractor unit shown in Fig., when the switch is in position $$2.$$ $$.....$$ using $$.....$$ arithmetic.