GATE CSE 2023
Q21.
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 \bar{A}+\bar{A}\cdot \bar{C}+A\cdot \bar{B}\cdot C ?Q22.
The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure.Match the functional equivalence of this circuit to one of the following options.Q23.
Consider the following statements regarding the front-end and back-end of a compiler. S1: The front-end includes phases that are independent of the target hardware. S2: The back-end includes phases that are specific to the target hardware. S3: The back-end includes phases that are specific to the programming language used in the source code. Identify the CORRECT option.Q24.
A keyboard connected to a computer is used at a rate of 1 keystroke per second. The computer system polls the keyboard every 10 ms (milli seconds) to check for a keystroke and consumes 100 \mu s (micro seconds) for each poll. If it is determined after polling that a key has been pressed, the system consumes an additional 200 \mu s to process the keystroke. Let T_1 denote the fraction of a second spent in polling and processing a keystroke. In an alternative implementation, the system uses interrupts instead of polling. An interrupt is raised for every keystroke. It takes a total of 1 ms for servicing an interrupt and processing a keystroke. Let T_2 denote the fraction of a second spent in servicing the interrupt and processing a keystroke. The ratio \frac{T_1}{T_2} is ______ . (Rounded off to one decimal place)Q25.
Let SLLdel be a function that deletes a node in a singly-linked list given a pointer to the node and a pointer to the head of the list. Similarly, let DLLdel be another function that deletes a node in a doubly-linked list given a pointer to the node and a pointer to the head of the list. Let n denote the number of nodes in each of the linked lists. Which one of the following choices is TRUE about the worst-case time complexity of SLLdel and DLLdel?Q26.
Let A=\begin{bmatrix} 1 & 2 & 3 &4 \\ 4& 1& 2 &3 \\ 3& 4 & 1 &2 \\ 2 &3 &4 &1 \end{bmatrix} and B=\begin{bmatrix} 3& 4 & 1 &2 \\ 4& 1& 2 &3 \\ 1 & 2 & 3 &4 \\ 2 &3 &4 &1 \end{bmatrix}Let det(A) and det(B) denote the determinants of the matrices A and B, respectively. Which one of the options given below is TRUE?Q27.
Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____Q28.
A 4 kilobyte (KB) byte-addressable memory is realized using four 1 KB memory blocks. Two input address lines (IA4 and IA3) are connected to the chip select (CS) port of these memory blocks through a decoder as shown in the figure. The remaining ten input address lines from IA11-IA0 are connected to the address port of these blocks. The chip select (CS) is active high. The input memory addresses (IA11-IA0), in decimal, for the starting locations (Addr=0) of each block (indicated as X1, X2, X3, X4 in the figure) are among the options given below. Which one of the following options is CORRECT?Q29.
Consider a computer system with 57-bit virtual addressing using multi-level tree-structured page tables with L levels for virtual to physical address translation. The page size is 4 KB (1 KB = 1024 B) and a page table entry at any of the levels occupies 8 bytes. The value of L is ______.Q30.
Consider the following two-dimensional array D in the C programming language, which is stored in row-major order: int D[128][128]; Demand paging is used for allocating memory and each physical page frame holds 512 elements of the array D. The Least Recently Used (LRU) page-replacement policy is used by the operating system. A total of 30 physical page frames are allocated to a process which executes the following code snippet: for (int i = 0; i < 128; i++) for (int j = 0; j < 128; j++) D[j][i] *= 10; The number of page faults generated during the execution of this code snippet is _____.