Chapter 2.4, Problem 2.50PP

A.

Program Plan Intro

Fractional binary numbers:

If each binary digit or bit b_i ranges between “0” and “1”, then the notation represented by the below equation

$\text{b }={\displaystyle \sum _{\text{i }=\text{ -n}}^{\text{m}}{\text{2}}^{\text{i}}\times {\text{b}}_{\text{i}}}$

Round-to-even rule:

• This rule rounding can be used even when user are not rounding to a entire number. The rounding can be calculated by using whether the least significant digit is even or odd.
• To binary fractional number, the round-to-even can be used by considering least significant value “0” to be even and “1” to be odd.

Example:

The example for round-to-even is shown below:

Consider a binary number is “10.00011₂” that is fractional $\text{2}\frac{\text{3}}{\text{32}}$ down to “10.00₂”.

• From the above binary number, the decimal for “10” is “2”.
• Here the rounding the values nearest to 2 bits to the right of the binary point.
• Hence, the result after rounding is “10.00₂”.

B.

Program Plan Intro

Fractional binary numbers:

If each binary digit or bit b_i ranges between “0” and “1”, then the notation represented by the below equation

$\text{b }={\displaystyle \sum _{\text{i }=\text{ -n}}^{\text{m}}{\text{2}}^{\text{i}}\times {\text{b}}_{\text{i}}}$

Round-to-even rule:

• This rule rounding can be used even when user are not rounding to a entire number. The rounding can be calculated by using whether the least significant digit is even or odd.
• To binary fractional number, the round-to-even can be used by considering least significant value “0” to be even and “1” to be odd.

Example:

The example for round-to-even is shown below:

Consider a binary number is “10.00011₂” that is $\text{2}\frac{\text{3}}{\text{32}}$ down to “10.00₂”.

• From the above binary number, the decimal for “10” is “2”.
• Here the rounding the values nearest to 2 bits to the right of the binary point.
• Hence, the result after rounding is “10.00₂”.

C.

Program Plan Intro

Fractional binary numbers:

If each binary digit or bit ${\text{b}}_{\text{i}}$ ranges between “0” and “1”, then the notation represented by the below equation.

$\text{b }={\displaystyle \sum _{\text{i }=\text{ -n}}^{\text{m}}{\text{2}}^{\text{i}}\times {\text{b}}_{\text{i}}}$

Round-to-even rule:

• This rule rounding can be used even when user are not rounding to a entire number. The rounding can be calculated by using whether the least significant digit is even or odd.
• To binary fractional number, the round-to-even can be used by considering least significant value “0” to be even and “1” to be odd.

Example:

The example for round-to-even is shown below:

Consider a binary number is “10.00011₂” that is $\text{2}\frac{\text{3}}{\text{32}}$ down to “10.00₂”.

• From the above binary number, the decimal for “10” is “2”.
• Here the rounding the values nearest to 2 bits to the right of the binary point.
• Hence, the result after rounding is “10.00₂”.

D.

Program Plan Intro

Fractional binary numbers:

If each binary digit or bit b_i ranges between “0” and “1”, then the notation represented by the below equation

$\text{b }={\displaystyle \sum _{\text{i }=\text{ -n}}^{\text{m}}{\text{2}}^{\text{i}}\times {\text{b}}_{\text{i}}}$

Round-to-even rule:

• This rule rounding can be used even when user are not rounding to a entire number. The rounding can be calculated by using whether the least significant digit is even or odd.
• To binary fractional number, the round-to-even can be used by considering least significant value “0” to be even and “1” to be odd.

Example:

The example for round-to-even is shown below:

Consider a binary number is “10.00011₂” that is $\text{2}\frac{\text{3}}{\text{32}}$ down to “10.00₂”.

• From the above binary number, the decimal for “10” is “2”.
• Here the rounding the values nearest to 2 bits to the right of the binary point.
• Hence, the result after rounding is “10.00₂”.