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ECE 2030a Quiz #4 Spring 2007

Name: Student #:

* Closed Book * No Notes * No Calculators *

1. (4 points) Perform each of the following. Write your answer in the box at the right edge.

a. Express the decimal value ( 76) using an 8-bit,

sign-magnitude binary representation.

b. Express the decimal value ( 76) using an 8-bit,2s-complement binary representation.

c. What decimal value corresponds to the 6-bit,2s-complement binary representation 110101 ?

d. What range of values can be represented by an

n-bit 2's-complement binary number?

2. (6 points) Assuming 5-bit 2s-complement integer arithmetic, perform the following binary

additions or subtractions. Write your answers in the boxes provided for each problem andcircle the answers indicating the value of the carry-out bit and whether or not overflow

occurred.

0 1 1 0 1 1 0 1 1 0 1 1 0 1 1

+ 1 1 1 0 1 + 1 0 1 1 1 - 0 1 1 1 0

to

carry-out: 0 1 carry-out: 0 1

overflow: yes no overflow: yes no overflow: yes no

8/7/2019 sp07quiz4

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ECE 2030a Quiz #4 Spring 2007

Name: Student #:

* Closed Book * No Notes * No Calculators *

1. (4 points) Perform each of the following. Write your answer in the box at the right edge.

a. Express the decimal value ( 86) using an 8-bit,

sign-magnitude binary representation.

b. Express the decimal value ( 86) using an 8-bit,2s-complement binary representation.

c. What decimal value corresponds to the 6-bit,2s-complement binary representation 101101 ?

d. What range of values can be represented by an

n-bit 2's-complement binary number?

2. 6 points) Assuming 5-bit 2s-complement integer arithmetic, perform the following binary

additions or subtractions. Write your answers in the boxes provided for each problem andcircle the answers indicating the value of the carry-out bit and whether or not overflow

occurred.

1 0 1 1 1 1 1 1 0 1 1 1 0 1 1

+ 1 0 1 1 0 + 0 1 1 0 1 - 0 1 1 0 1

to

carry-out: 0 1 carry-out: 0 1

overflow: yes no overflow: yes no overflow: yes no

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ECE 2030a Quiz #4 Spring 2007

Name: SOLUTION Student #:

* Closed Book * No Notes * No Calculators *

1. (4 points) Perform each of the following. Write your answer in the box at the right edge.

e. Express the decimal value ( 76) using an 8-bit,

sign-magnitude binary representation.

10110100

11001100

2n-1

to 2n-1

1

11

f. Express the decimal value ( 76) using an 8-bit,2s-complement binary representation.

g. What decimal value corresponds to the 6-bit,2s-complement binary representation 110101 ?

h. What range of values can be represented by an

n-bit 2's-complement binary number?

2. (6 points) Assuming 5-bit 2s-complement integer arithmetic, perform the following binary

additions or subtractions. Write your answers in the boxes provided for each problem andcircle the answers indicating the value of the carry-out bit and whether or not overflow

occurred.

0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 = 1 1 0 1 1

+ 1 1 1 0 1 + 1 0 1 1 1 - 0 1 1 1 0 + 1 0 0 1 0

0 1 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1

carry-out: 0 1 carry-out: 0 1

overflow: yes no overflow: yes no overflow: yes no

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