Q. What is the minimum number of 2-input NOR gates required to implement a 4-variable function expressed in sum-of-minterms form as f = Σ (0, 2, 5, 7, 8, 10, 13, 15)? Assume that all the inputs and their complements are available. Answer: . Ans: K-map for given, f = Σ(0, 2, 5, 7, 8, […]
Q. Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is. Solution: You need at least 3 switches of Ethernet are required to connect 15 computers.
Q. Let Σ be the set of all bijections from {1, … , 5} to {1, … , 5}, where 𝑖𝑑 denotes the identity function, i.e. 𝑖𝑑(𝑗) = 𝑗, ∀𝑗. Let ∘ denote composition on functions. For a string 𝑥 =𝑥1 𝑥2 ⋯ 𝑥𝑛 ∈ Σ𝑛, 𝑛 ≥ 0 , let 𝜋(𝑥) = 𝑥1 ∘ 𝑥2
Q. Suppose 𝑌 is distributed uniformly in the open interval (1,6). The probability that the polynomial 3𝑥2 + 6𝑥𝑌 + 3𝑌 + 6 has only real roots is (rounded off to 1 decimal place) Solution: For a quadratic polynomial ax2 + bx + c = 0. There are three condition: b2 – 4ac > 0
Q. Let 𝑇 be a full binary tree with 8 leaves. (A full binary tree has every level full.) Suppose two leaves 𝑎 and 𝑏 of 𝑇 are chosen uniformly and independently at random. The expected value of the distance between 𝑎 and 𝑏 in 𝑇 (i.e., the number of edges in the unique path
Q. A certain processor deploys a single-level cache. The cache block size is 8 words and the word size is 4 bytes. The memory system uses a 60-MHz clock. To service a cache miss, the memory controller first takes 1 cycle to accept the starting address of the block, it then takes 3 cycles to
Q. The index node (inode) of a Unix-like file system has 12 direct, one single-indirect and one double-indirect pointers. The disk block size is 4 kB, and the disk block address is 32-bits long. The maximum possible file size is (rounded off to 1 decimal place) ____________GB. Solution: No. of Disk block pointers = 4kB/32bits
Q. Consider the following four processes with arrival times (in milliseconds) and their length of CPU bursts (in milliseconds) as shown below: Process P1 P2 P3 P4 Arrival time 0 1 3 4 CPU burst time 3 1 3 Z These processes are run on a single processor using preemptive Shortest Remaining Time First scheduling
Q. Consider the following statements: Which of the above statements are TRUE? (A) I, II and III (B) I, II and IV (C) I, III and IV (D) II, III and IV Ans: I, II and III
Q. Consider the following snapshot of a system running 𝑛 concurrent processes. Process 𝑖 is holding 𝑋𝑖 instances of a resource R, 1 ≤ 𝑖 ≤ 𝑛. Assume that all instances of R are currently in use. Further, for all 𝑖, process 𝑖 can place a request for at most 𝑌𝑖 additional instances of R
