Homework 3 - CS 2204 - Spring 2024
1. Given the following 2’s complement binary numbers, determine their decimal value. Show your working.
a. 10001010
b. 01101101
c. 11110010
d. 10110101
2. Given the following decimal numbers, determine their 12–bit binary value in 2’s complement. Show your working.
a. –376
b. 983
c. –12
d. –1311
3. Perform. the following operations involving n–bit 2’s complement numbers and indicate whether arithmetic overflow occurs. You can check your answers by converting to decimal sign magnitude form. Show your working.
a. 1011 + 0101
b. 1001 – 0110
c. 001110 – 101001
d. 010100 – 010110
e. 11110000 + 00011111
4. Design a circuit that converts 4–bit numbers from 2’s complement to signed magnitude binary. You may use MUXes, AND/OR/NOT’s, and 4–bit adders. An n-bit adder is defined with two n-bit inputs x[n-1:0] and y[n-1:0] and cin, and with outputs s[n-1:0] and cout.
5. Design a circuit for the following: Given two 4–bit numbers x and y, count the number of bits that are different between x and y.
6. Design a circuit to compute (x+y)%13 for two 4–bit unsigned inputs x and y. You may use MUXes, AND/OR/NOT’s, and 4– or 5–bit unsigned adders.
7. (Extra Credit) Prove that given an n–bit binary number X = [Xn – 1, …, X0] in 2’s complement,