a) Design a combinational circuit for a new brand of computers that will take a 4-bit binary number as input and output 1 if the input contains at least 2 zeros. For example:
i) Input 0000: output 1 (4 zeros)
ii) Input 0001: output 1 (3 zeros)
iii) Input 0011: output 1 (2 zeros)
iv) Input 0111: output 0 (1 zero)
b) Draw the minimum cost AND-OR implementation for the function below. Input variables are available in true and complement forms.
F(A,B,C,D)= ?m(1,3,6,7,11,14,15)+D(5,9,10)
c) An electronic gate has a digital logic circuit whose output is a "1" if majority of the input variables are 1's. The output is a zero (0) otherwise. Using a truth table find the Boolean function implemented by a three (3) input variable majority gate Design the electronic gate
a) Design a combinatorial circuit that will be able to detect prime numbers given as input in binary. The input to the system will be any 4 bit binary number. The output of the circuit should be a single bit that will be 1 (high) if the input is a prime number and 0 (low) if the input is not a prime number. For example, if the input to the circuit is 0101 the output should be 1. Again if the input is 1010, the output should be 0.
b) Implement the function below together with the don't care condition given below using only two NOR gates. Assume that both the normal and complement inputs are available.
F(A,B,C,D) = ?m (1, 3, 5, 6)
d(A,B,C,D) = ?m (8, 10, 14, 15)
c) Design a function that will take a 3 bit binary number as input and the output will be "HIGH" if total number of 1s in input is less than or equal to total number of 0s and "LOW" otherwise.
