#### Assignment 5

##### Due: 9:00am, Thu Feb 23rd, 2017

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.

1. Convert the decimal number -31.75 into the IEEE 754 format for a single-precision floating-point number. (15 points)
2. Convert the following IEEE 754 single-precision floating-point register into a decimal number: 1 10000010 01000000000000000000000. (15 points)
3. Convert the following IEEE 754 double-precision floating-point register into a decimal number: 1 10000000001 1000000000000000000000000000000000000000000000000000. (15 points)
4. What is the result of adding the following two IEEE 754 single-precision floating-point registers (show the steps)? (15 points)
0 10000011 10000000000000000000000
0 10000001 01000000000000000000000
5. Compute the truth table for a logic block that takes in a 3-bit input and computes the 2's complement of that input (a 3-bit output). Express this logic block with the correct set of sum-of-product Boolean equations. (20 points)
6. Draw the state transition table for the sequential circuit that implements the following function in a self-driving car. In every second, the car's position within the lane is determined with cameras and fed as input to the sequential circuit. Accordingly, the car's steering wheel is moved to one of 2 positions: Left, Right. The car itself can be "Middle of a lane", "Drifting to the right edge of the lane", and "Drifting to the left edge of the lane". If the car is in the "Middle", the steering position is left unchanged. If the car is drifting to the edge of the lane, the steering is moved away from the edge. (20 points)