Assignment 5

Note: Make reasonable assumptions where necessary and clearly state them. Feel free to

discuss problems with classmates, but the only written material that you may consult while

writing your solutions are the textbook and lecture slides/videos. Solutions should be

uploaded as a single pdf file on Canvas. Show your solution steps so you receive partial

credit for incorrect answers and we know you have understood the material. Don’t just

show us the final answer.

1. Convert the decimal number -26.3125 into the IEEE 754 format for a single-precision

floating-point number. (20 points)

2. Convert the following IEEE 754 single-precision floating-point register into a decimal

number: 1 10000111 11010000000000000000000. (20 points)

3. Convert the following IEEE 754 double-precision floating-point register into a decimal

number: 1 10000000011

1010000000000000000000000000000000000000000000000000. (20 points)

4. What is the result of adding the following two IEEE 754 single-precision floating-point

registers? Show your steps as you perform the math in binary and produce the final

IEEE 754 value that will be placed in the register. (20 points)

0 10000010 00100000000000000000000

0 10000101 11000000000000000000000

5. Compute the truth table for a logic block that takes in a 3-bit input and produces a 2-

bit output that represents the number of 1’s in the 3-bit input. For example, if the

input is 101, the output should be 10, i.e., there are two 1’s in the input 101. Express

each output bit with a sum-of-product Boolean equation. (20 points)