GATE CS Digital Logic questions

Zero has two representations in

The number of full and half-adders required to add $16$-bit numbers is

Which of the following sets of component(s) is/are sufficient to implement any arbitrary Boolean function?

Consider the circuit shown below. In a certain steady state, the line $Y$ is at $'1'$. What are the possible values of $A, B$ and $C$ in this state?

The maximum gate delay for any output to appear in an array multiplier for multiplying two $n$ bit numbers is

Booth's coding in $8$ bits for the decimal number $-57$ is:

Which of the following functions implements the Karnaugh map shown below?

Which of the following expressions is not equivalent to $\bar{x}$?

Suppose the domain set of an attribute consists of signed four digit numbers. What is the percentage of reduction in storage space of this attribute if it is stored as an integer rather than in character form?

Which of the following operations is commutative but not associative?

The function represented by the Karnaugh map given below is

The octal representation of an integer is $(342)_8$. If this were to be treated as an eight-bit integer in an $8085$ based computer, its decimal equivalent is

The threshold level for logic 1 in the TTL family is

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

What happens when a bit-string is XORed with itself $n$-times as shown: $\left[B \oplus (B \oplus ( B \oplus (B \dots n \text{ times}\right]$

Let $f=(\bar{w} + y)(\bar{x} +y)(w+\bar{x}+z)(\bar{w}+z)(\bar{x}+z)$ Express $f$ as the minimal sum of products. Write only the answer. If the output line is stuck at $0$, for how many input combinations will the value of $f$ be correct?

Consider a logic circuit shown in figure below. The functions $f_1, f_2 \text{ and } f$ (in canonical sum of products form in decimal notation) are : $f_1 (w, x, y, z) = \sum 8, 9, 10$ $f_2 (w, x, y, z) = \sum 7, 8, 12, 13, 14, 15$ $f (w, x, y, z) = \sum 8, 9$ The function $f_3$ is

Given $\sqrt{(224)_r} =(13)_r$. The value of the radix $r$ is:

Let $f(x, y, z)=\bar{x} + \bar{y}x + xz$ be a switching function. Which one of the following is valid?

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