Steps to convert binary number into decimal value: If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number. The sign of the decimal value is negative, if the LSB is one. If “1” is appeared in the LSB, compute 2’s complement of the decimal value. To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result. Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”. The user includes a minus sign in front of the decimal value, if the original number is negative.

Question

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Answer 1

Question

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

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Answer 2

Question

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Answer 6

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

Answer 7

Chapter 2, Problem 10E

a.

Program Plan Intro

Steps to convert binary number into decimal value:

If “0” is appeared in the Left most Significant Bit (LSB), it denotes the sign of the decimal value is positive. Binary number can be directly converted into decimal number.

The sign of the decimal value is negative, if the LSB is one.

If “1” is appeared in the LSB, compute 2’s complement of the decimal value.

To find 2’s complement, transform the bits from “0” to “1” and from “1” to “0”, which gives 1’s complement and then add “1” to the result.

Decimal value can be obtained by adding the powers of “2”, which having the coefficients “1”.

The user includes a minus sign in front of the decimal value, if the original number is negative.

Answer 8

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

Answer 9

b.

Explanation of Solution

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1

Answer 10

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

Answer 11

c.

Explanation of Solution

Conversion from the binary number “11111110” to decimal value:

The LSB of the binary number is “1” and it represents the sign of the decimal value is negative.

The user should find the 2’s complement representation as follows,

Find the 1’s complement by transforming the bits from “0” to “1” and from “1” to “0”.

Hence, the 1’s complement of the number is ‘00000001”.

Add “1” to the above result. “00000001+1”, which gives “00000010”.

The 2’s complement representation of the positive number is “00000010”...

Answer 12

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Answer 13

d.

Explanation of Solution

Conversion from the binary number “0011100111010011” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

215×0+214×0+213×1+212×1+211×1+210×0+29×0+28×1+27×1+26×1+2

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Check out a sample textbook solution

See solution

Answer 17

Ch. 2 - Prob. 1E Ch. 2 - Prob. 2E Ch. 2 - Prob. 3E Ch. 2 - Prob. 4E Ch. 2 - Prob. 5E Ch. 2 - Prob. 6E Ch. 2 - Prob. 7E Ch. 2 - Prob. 8E Ch. 2 - Prob. 9E Ch. 2 - Prob. 10E

Explanation of Solution

Conversion from the binary number “01011010” to decimal value: The LSB of the binary number is “0” and it represents the sign of the decimal value is positive. Hence, the user can directly compute the magnitude value as follows, 27×0+26×1+25×0+24×1

Explanation of Solution

Explanation of Solution

Want to see the full answer?

Chapter 2 Solutions

Conversion from the binary number “01011010” to decimal value:

The LSB of the binary number is “0” and it represents the sign of the decimal value is positive.

Hence, the user can directly compute the magnitude value as follows,

27×0+26×1+25×0+24×1