## Description

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)