CPSC 231: Assignment 2 (Worth 3%)

New Concepts to be applied for the assignment

• Converting numbers that are in different bases: binary, octal, decimal and hexadecimal
• Converting from decimal and binary to signed binary representations
• Performing common logical operations

Part I: Number conversions (4 marks: Show all your work)

1. 11001₂ (binary) to octal

        Answer:

2. 32₁₀ (decimal) to hexadecimal

          Answer:

3. 32₈ (octal) to decimal

        Answer:

4. 12.75₁₀ (decimal) to binary

        Answer:

Part II: Non-decimal based math (3 marks: Show your work)

Perform the following binary additions and subtractions using regular base two subtraction and not by using complements.  Assume a four bit architecture. 

Part III: Complements (3 marks)

Perform the necessary conversions between the three binary representations (using five bits) in order to fill in the missing values in the table below.

Part IV: Non-decimal based math (4 marks: Show your work)

Perform the following subtractions via the negate and add technique using 4 bits.   Show the final result both in binary and in the appropriate signed representation.                                                                                  

Show your work here:

Answer (One's complement): 

Answer (Binary):                   

Show your work here:

Answer (Two' complement): 

Answer (Binary):                 

Part V: Logic (5 marks)

Perform the following logical operations.

AND

	T	F	T	F	T
AND	T	T	T	F	T

 

OR

	T	F	T	F	T
OR	T	T	T	F	T

 

XOR

	T	F	T	F	T
XOR	T	T	T	F	T

 

NAND

	T	F	T	F	T
NAND	T	T	T	F	T

 

NOR

	T	F	T	F	T
NOR	T	T	T	F	T