CPSC 217: Assignment 2 (Worth 6%)
Scoring
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Score |
50-51 |
48-49 |
44-47 |
40-43 |
36-39 |
31-35 |
27-30 |
23-26 |
18-22 |
13-17 |
8-12 |
0-7 |
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Letter |
A |
A- |
B+ |
B |
B- |
C+ |
C |
C- |
D+ |
D |
D- |
F |
New Concepts to be applied for the assignment
- Converting numbers that are in different bases: binary, octal, decimal
and hexadecimal
- Binary math
- Converting from binary to signed binary representations
- Performing subtractions via the complement and add technique
- Storing real numbers as floating values
- Performing common logical operations
Part I: Number conversions (12 marks: Half marks for the answer, half
marks for showing your work)
- 1010102 (binary) to octal
Answer:
- 11010010002 (binary) to hexadecimal
Answer:
- 5816 (hexadecimal) to octal
Answer:
- 2910 (decimal) to hexadecimal
Answer:
- 10.2510 (decimal) to binary
Answer:
- 176.48 (octal) to decimal
Answer:
Part II: Non-decimal based math (6 marks: Half marks for the answer, half
marks for showing your work)
Perform the following binary additions and subtractions (using regular base
two subtraction employing a borrow if necessary) and not by using
complements.
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11110 |
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10100 |
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10000 |
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+11010 |
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-01010 |
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-00010 |
| Binary result |
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Part III: Complements (6 marks: 1 mark for each empty cell).
Perform the necessary conversions in order to fill in the missing values in
the table below.
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Number system |
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Original binary value |
Ones complement value |
Twos complement value |
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First example |
010010 |
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Second example |
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100111 |
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Third example |
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111111 |
Part IV: Non-decimal based (15 marks: For each conversion 1 mark
for the binary value, 1 mark for the value as the appropriate complement, 1 mark for the
decimal value, 2 marks for showing your work).
Perform the following subtractions via the complement and add technique
using 4 bits.
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One's complement approach |
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710 |
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- |
510 |
Show your work here:
Answer (Ones complement):
Answer (Binary):
Answer (Decimal):
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One's complement approach |
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-510 |
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-510 |
Show your work here:
Answer (Ones complement):
Answer (Binary):
Answer (Decimal):
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Two's complement approach |
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310 |
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- |
410 |
Show your work here:
Answer (Twos complement):
Answer (Binary):
Answer (Decimal):
Part V: Floating point (6 marks for the correct mantissa and exponent
values)
For this part
of the assignment you are to assume that the computer will store real numbers in
floating point form. The computer can store up to 5 digits for the mantissa and
2 digits for the exponent. Based on the input you are to determine what will be
stored in the mantissa and the exponent.
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| Number input |
Mantissa |
Exponent |
| 63851 |
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| 1050 |
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| 645367 |
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Part VI: Logic (6 marks for the correct answer)
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T |
F |
T |
F |
F |
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AND |
F |
F |
T |
T |
F |
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T |
F |
T |
F |
F |
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OR |
F |
F |
T |
T |
F |
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T |
F |
T |
F |
F |
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XOR |
T |
F |
T |
F |
F |
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T |
F |
T |
F |
F |
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NOT |
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T |
F |
T |
F |
F |
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NAND |
F |
F |
T |
T |
F |
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T |
F |
T |
F |
F |
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NOR |
F |
F |
T |
T |
F |
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As a reminder, you are not allowed to work in groups for this class.
Copying the work of another student will be regarded as academic misconduct
(cheating). For additional details about what is and is not okay for this
class please refer to the following link