One's complement representations of integers is used to simplify computer arithmetic, while representing both positive and negative values in bits (base 2). A n-bit number represents positive and negative integers with absolute value less than 2"-1. The leftmost bit is used to represent the sign. A 0 bit in this position is used for positive integers, and a 1 bit in this position is used for negative integers. When a value is negative, the magnitude of the value is represented by the rest of the bits, but the l's and 0's flipped. For example: The number –5 expressed in 4-bit 1s-complement is 1010: the first bit indicates it's a negative number. The last 3 bits, when flipped to 101, is the base-2 representation of 510- (a) Find the one's complement representations, using bit strings of length six, of the following integers. i. 19 ii. 75 i. ii. iii. -72 iii. iv. -1 iv. (b) What integer does each of the following one's complement representations of length five represent? i. 111000 i. ii. 001100 iii. 101110 ii. iii. iv. 100101 iy. ii. What is the smallest number that can be represented by a 9-bit number in l's-complement?

Systems Architecture
7th Edition
ISBN:9781305080195
Author:Stephen D. Burd
Publisher:Stephen D. Burd
Chapter3: Data Representation
Section: Chapter Questions
Problem 23VE: ___________ occurs when the result of an arithmetic operation exceeds the number of bits available...
icon
Related questions
Question
One's complement representations of integers is used to simplify computer arithmetic, while representing both
positive and negative values in bits (base 2). A n-bit number represents positive and negative integers with absolute
value less than 2"-1, The leftmost bit is used to represent the sign. A 0 bit in this position is used for positive integers,
and a 1 bit in this position is used for negative integers. When a value is negative, the magnitude of the value is
represented by the rest of the bits, but the l's and O's flipped.
For example: The number –5 expressed in 4-bit 1s-complement is 1010: the first bit indicates it's a negative number.
The last 3 bits, when flipped to 101, is the base-2 representation of 510.
(a) Find the one's complement representations, using bit strings of length six, of the following integers.
i. 19
i.
ii. 75
ii.
iii. -72
ii.
iv. -1
iv.
(b) What integer does each of the following one's complement representations of length five represent?
i. 111000
ii. 001100
i.
ii.
iii. 101110
ii.
iv. 100101
iy.
ii.
What is the smallest number that can be represented by a 9-bit number in l's-complement?
Transcribed Image Text:One's complement representations of integers is used to simplify computer arithmetic, while representing both positive and negative values in bits (base 2). A n-bit number represents positive and negative integers with absolute value less than 2"-1, The leftmost bit is used to represent the sign. A 0 bit in this position is used for positive integers, and a 1 bit in this position is used for negative integers. When a value is negative, the magnitude of the value is represented by the rest of the bits, but the l's and O's flipped. For example: The number –5 expressed in 4-bit 1s-complement is 1010: the first bit indicates it's a negative number. The last 3 bits, when flipped to 101, is the base-2 representation of 510. (a) Find the one's complement representations, using bit strings of length six, of the following integers. i. 19 i. ii. 75 ii. iii. -72 ii. iv. -1 iv. (b) What integer does each of the following one's complement representations of length five represent? i. 111000 ii. 001100 i. ii. iii. 101110 ii. iv. 100101 iy. ii. What is the smallest number that can be represented by a 9-bit number in l's-complement?
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Binary numbers
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Systems Architecture
Systems Architecture
Computer Science
ISBN:
9781305080195
Author:
Stephen D. Burd
Publisher:
Cengage Learning