Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Find the two’s complement representations, using bit strings of length six, of the following integers.
a) 22 b) 31 c) −7 d) −19

The one’s complement representations, using bit strings of length six

$a) 010110 b) 011111 c) 111001 d) 101101$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1:

a) You obtain the binary expansion of an integer by consecutively dividing the integer by 2 until you obtain 0

$\begin{aligned} 22 = 2.11 + 0 \\ 11 = 2.5 + 1 \\ 5 = 2.2 + 1 \\ 2 = 2.2 + 0 \\ 1 = 2.0 + 1 \end{aligned}$

The successive remainders of each division represents the binary expansion from right to left.

10110

Since 22 is positive, we add a 0 to the left of the binary expansions (to signify a positive number)

$010110$

Step 2:

b) You obtain the binary expansion of an integer by consecutively dividing the integer by 2 until you obtain 0

$\begin{aligned} 31 = 2.15 + 1 \\ 15 = 2.7 + 1 \\ 7 = 2.3 + 1 \\ 3 = 2.1 + 1 \\ 1 = 2.0 + 1 \end{aligned}$

c) The successive remainders of each division represents the binary expansion from right to left.

11111

Since 31 is positive, we add a 0 to the left of the binary expansions (to signify a positive number)

011111

Step 3:

d) You obtain the binary expansion of an integer by consecutively dividing the integer by 2 until you obtain 0

$\begin{aligned} 7 = 2.3 + 1 \\ 3 = 2.1 + 1 \\ 1 = 2.0 + 1 \end{aligned}$

The successive remainders of each division represents the binary expansion from right to left.

111

Since two’s complement needs to contain 6 bits, the expansion will need to contain 5 bits, thus add 0’s in front of the binary expansion until we obtain 5 bits.

00111

Since -7 is negative, subtract 00111 from 100000

$(100000)_{2} - (00111)_{2} = (11001)_{2}$

Note: you could determine the difference by using $(00111)_{2} + (11001)_{2} = (100000)_{2}$

Since -7 is negative, we add a 1 to the left of the previous result (to signify a negative number).

111001

Step 4:

e) You obtain the binary expansion of an integer by consecutively dividing the integer by 2 until you obtain 0

$\begin{aligned} 19 = 2.9 + 1 \\ 9 = 2.4 + 1 \\ 4 = 2.2 + 1 \\ 2 = 2.1 + 0 \\ 1 = 2.0 + 1 \end{aligned}$

The successive remainders of each division represents the binary expansion from right to left.

10011

Since -19 is negative, subtract 10011 from 100000

$(100000)_{2} - (10011)_{2} = (01101)_{2}$

Note: you could determine the difference by using $(10011)_{2} + (01101)_{2} = (100000)_{2}$

Since -19 is negative, we add a 1 to the left of the previous result (to signify a negative number).

101101

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Find the two’s complement representations, using bit strings of length six, of the following integers.
a) 22 b) 31 c) −7 d) −19

Step by Step Solution

Step 1:

Step 2:

Step 3:

Step 4:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Find the two’s complement representations, using bit strings of length six, of the following integers. a) 22 b) 31 c) −7 d) −19

Step by Step Solution

Step 1:

Step 2:

Step 3:

Step 4:

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths

Find the two’s complement representations, using bit strings of length six, of the following integers.
a) 22 b) 31 c) −7 d) −19