Chapter 6.1, Problem 58E

a.

To determine

To calculate: The number of kilobytes are in one terabyte?

Unit	kilobyte	megabyte	gigabyte	terabyte
Number of bytes	$2^{10}$	$2^{20}$	$2^{30}$	$2^{40}$

Answer to Problem 58E

1 terabyte = $2^{30}$ kilobytes

Explanation of Solution

Given information: From the table we can see that 1 terabyte = $2^{40}$ bytes and 1 kilobyte = $2^{10}$ bytes.

Calculation: we have 1 kilobyte = $2^{10}$ bytes

Now multiplying both sides by $2^{30}$ in above equation, we get

1 kilobyte $*2^{30}=2^{10}*2^{30}$ bytes

  $2^{30}*$ 1 kilobyte = $2^{40}$ bytes

and we know that, 1 terabyte = $2^{40}$ bytes

from above 2 equations we can see that right side of both equations are same so we can say that left sides are also equal, hence

1 terabyte = $2^{30}$ kilobytes

b.

To determine

To calculate: The numbers of megabytes are in 16 gigabytes.

Unit	kilobyte	megabyte	gigabyte	terabyte
Number of bytes	$2^{10}$	$2^{20}$	$2^{30}$	$2^{40}$

Answer to Problem 58E

16 gigabyte $=2^{14}$ megabytes

Explanation of Solution

Given information: From the above table we can see that 1 megabyte = $2^{20}$ bytes and 1 gigabyte = $2^{30}$ bytes

Calculation: we have 1 megabyte = $2^{20}$ bytes

Now multiplying both sides by $2^{10}$ in above equation , we get

1 megabyte $*2^{10}=2^{10}*2^{20}$ bytes

  $2^{10}*$ 1 megabyte = $2^{30}$

and we know that, 1 gigabyte = $2^{30}$ bytes

from above 2 equations we can see that right side of both equations are same so we can say that left sides are also equal, hence

1 gigabyte = $2^{10}$ megabytes

multiplying above equation both sides by 16, we get

16 gigabyte = $16*2^{10}$

  $=2^4*2^{10}$

  $=2^{14}$

hence 16 gigabyte $=2^{14}$ megabytes

Conclusion:

c.

To determine

To calculate How can you convert the number of bytes in each unit of measure given in the table to bits? Can you still use a base of 2? Explain

Unit	Kilobyte	megabyte	gigabyte	terabyte
Number of bytes	$2^{10}$	$2^{20}$	$2^{30}$	$2^{40}$

Answer to Problem 58E

We can convert the measurements to bits by multiplying $2^3$ to each exponent. Still we can write it in base of 2.

Explanation of Solution

Given information: 1 byte = 8 bits

Calculation: we can write $8=2^3$

so still we can use a base of 2. As we know 1 byte = 8 bits = $2^3$ bits

so to find the number of bits in each measurement, just multiply each measurement by $2^3$ we get our answer.