CSC 156 Spring 2025 - Homework 6 (100 pts. total)
Assigned Mon Mar 10, due Mon Mar 24
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:
[20 pts.] Question 1: Draw a circuit diagram for the Boolean expression
z x y +
z x y +
z x y + z x y. This represents the Carry Out bit, C(z,x,y), for a full-adder circuit.
[10 pts.] Question 2a: Evaluate C(1,0,1) using the expression in Question 1.
[10 pts.] Question 2b: C(z,x,y) can also be represented by the expression xy + zy + zx. Evaluate C(1,0,1) again using this expression.
[20 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 a signed integer in two's complement notation. Convert this number to decimal format.
Last Modified: 3/7/25