CSC 156 Spring 2024 - Homework 6 (100 pts. total)
Assigned Tue Mar 26, due Mon Apr 1
BEFORE STARTING THIS ASSIGNMENT:
Before starting the exercises given below for each section, please make sure to read each Zybook section and check your understanding (by doing the participation exercises).
FOR ALL QUESTIONS IN THIS ASSIGNMENT:
Answer each question. *Make sure to justify your answer for all questions. Do NOT just state the answer.*
THE ASSIGNMENT:
[18 pts.] Question 1: In class, we showed that a Boolean function for the carry bit is C(z,x,y) =
z x y +
z x y +
z x y + z x y. Fill in the blanks on this attached proof, where you use the Laws of Boolean Algebra (section 2.1) to show that this is equivalent to C(z,x,y) = xy + zy + zx.
[16 pts.] Question 2: Draw a circuit diagram for the Boolean function C(z,x,y) = xy + zy + zx, which represents the Carry Out bit for a full-adder circuit.
[16 pts.] Question 3: Draw a diagram of a circuit (using half-adder [H] and full-adder [F] circuits) that can be used
to add together two 3-bit numbers, and show the results of adding together 110 and 101 by writing the value corresponding to each wire.
[20 pts.] Question 4a: Find the 8-bit binary expression for 49 and for -49 (using the two's complement notation).
[10 pts.] Question 4b: Use binary addition to show that the sum of the binary numbers for 49 and -49 (found in part a) is the binary number 00000000. When justifying your work, be sure to clearly indicate where the digit '1' was carried.
[10 pts.] Question 5: The binary number 10101001 represents an unsigned integer. Convert this binary number to decimal format.
[10 pts.] Question 6: The binary number 10101001 represents a signed integer in two's complement notation. Convert this number to decimal format.
Last Modified: 3/28/24