Given two three bit numbers a2a1a0 and b2b1b0 and c, the carry in, the function that represents the carry generate function when these two numbers are added is:

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 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

A 4-bit carry lookahead adder, which adds two 4-bit numbers, is designed using AND, OR, NOT, NAND, NOR gates only. Assuming that all the inputs are available in both complemented and uncomplemented forms and the delay of each gate is one time unit, what is the overall propagation delay of the adder? Assume that the carry network has been implemented using two-level AND-OR logic.

Consider an array multiplier for multiplying two n bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

A 1-input, 2-output synchronous sequential circuit behaves as follows :

Let zk, nk denote the number of 0's and 1's respectively in initial k bits of the input (zk + nk = k). The circuit outputs 00 until one of the following conditions holds.

zk - nk = 2. In this case, the output at the k-th and

all subsequent clock ticks is 10.

nk - zk = 2. In this case, the output at the k-th and

all subsequent clock ticks is 01.

What is the minimum number of states required in the state transition graph of the above circuit?

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal count of (xy + xz') is 4. What are the minimum possible literal counts of the product-of-sum and sum-of-product representations respectively of the function given by the following Karnaugh map ? Here, X denotes "don't care"

A teacher conducts a monthly test for a group of 4 students. There are 3 subjects with maximum marks being 10 for each. Write C program to answer the following. Your program must work for all valid inputs and throw an error if invalid input is given.

(a) (1+2.5=3.5 marks) Variable declaration and Input acceptance: Ask the user to input marks of 3 subjects for 4 students. Must throw an error for invalid inputs. Marks with fractions are allowed with at most one digit after the dot. Marks such as 3, 3.5 (exactly one digit after the dot is allowed) are valid, whereas 3.45, 3.21 are invalid. Note that 3.20 is valid as it will be treated as 3.2.

(b) (1 mark) Computer Average for each subject for 4 students.

(c) (1.5 marks) Grade the students on all 3 subjects as per the following scheme. Grade S if marks is at least twice the average. Grade A if marks is at least average+3 and below the cut off of 'S'. Grade B if marks is exactly the average. Otherwise Grade C.

(d) (1+1.5+1.5=4 marks) Compute total marks for each student. Also, print the floor and ceil value of the total without using floor/ceil functions

Accept from the user 10 integers and a special integer x. Question: Check whether there exist a pair of integers y and z in the input whose sum is x, i.e., x = y + z. Additionally, print all such pairs. Logic: (3 marks) Write the logic below and trace your logic for the input; {1, 2, 3, 4, 5, 6, 1, 1, 0, 59}, x = 1. Further, write C program that implements this logic.