Computers and Technology, 04.12.2020 16:50 AllanCasey12

(Numerical Data Representation) How many bits per word are required to represent the following positive decimal integers: a.0 through 100b.0 through 255c.0 through 256d.0 through 10,000,000

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Answer from: Fangflora3

a. 7 bits

b. 8 bits

c. 9 bits

d. 24 bits

Explanation:

Required

Number of bits per word

The formula to get the number of bits per word is:

2^n = N

Where

n = bits

N = numbers

Solving (a) 0 to 100

There are 101 digits between 0 and 100 (inclusive)

So:

N = 101

Substitute 101 for N in 2^n = N

2^n = 101

101 can not be expressed as an exponent of 2.

So, we substitute 101 for the closest number greater than 101 that can be expressed as an exponent of 2.

So:

2^n = 128

Express 128 as an exponent of 2

2^n = 2^7

Apply law of indices

n = 7

Hence, 7 bits are required

Solving (b): 0 through 255

There are 256 digits between 0 and 255 (inclusive)

So:

N = 256

Substitute 256 for N in 2^n = N

2^n = 256

Express 256 as an exponent of 2

2^n = 2^8

Apply law of indices

n = 8

Hence, 8 bits are required

Solving (c): 0 through 256

There are 257 digits between 0 and 256 (inclusive)

So:

N = 257

Substitute 257 for N in 2^n = N

2^n = 257

257 can not be expressed as an exponent of 2.

So, we substitute 257 for the closest number greater than 101 that can be expressed as an exponent of 2.

So:

2^n = 512

Express 512 as an exponent of 2

2^n = 2^9

Apply law of indices

n = 9

Hence, 9 bits are required

Solving (d): 0 through 10000000

There are 10000001 digits between 0 and 10000000 (inclusive)

So:

N = 10000000

Substitute 10000000 for N in 2^n = N

2^n = 10000000

10000000 can not be expressed as an exponent of 2.

So, we substitute 10000000 for the closest number greater than 101 that can be expressed as an exponent of 2.

So:

2^n = 16777216

Express 16777216 as an exponent of 2

$2^n = 2^{24$

Apply law of indices

n = 24

Hence, 24 bits are required

Answer from: Quest

solution:

the auto-correct option of the auto-correct tool enables you to add and delete words that do not follow abbreviation rules because:

it is a feature that allows outlook to correct common spelling and typing errors and to replace characters with symbols. we can also can use auto-correct as a shortcut, which means we can type a small string of characters and have those characters replaced by a longer string.

Answer from: Quest

Iwould try the first option, first then if that didn't work i would try the last option.

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(Numerical Data Representation) How many bits per word are required to represent the following posit...