#### Assignment 5

##### Due: 10:45am, Thu Feb 22nd, 2024

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 on Gradescope. 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.

Every homework has an automatic penalty-free 1.5 day extension to accommodate any covid/family-related disruptions. In other words, try to finish your homework by Thursday 10:45am to keep up with the lecture content, but if necessary, you may take until Friday 11:59pm.

1. Convert the decimal number -17.6875 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: 0 01111100 01110000000000000000000. (20 points)
3. Convert the following IEEE 754 double-precision floating-point register into a decimal number: 0 10000000111 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 10000110 01010000000000000000000
0 10000100 11000000000000000000000
5. Compute the truth table for a logic block that takes in a 3-bit input representing a binary unsigned number Y (values 0 to 7) and produces a 2-bit output X = Y modulo 3. Express each output bit (let's call them X1 and X2) with a sum-of-products Boolean equation. (20 points)