9. (Practice) Although the total number of bytes varies from computer to compute

Question

9. (Practice) Although the total number of bytes varies from computer to computer, memory sizes of millions and billions of bytes are common. In computer language, the letter M represents the number 1,048,576, which is 2 raised to the 20th power, and G represents 1,073,741,824, which is 2 raised to the 30th power. Therefore, a memory size of 4 MB is really 4 times 1,048,576 (4,194,304 bytes), and a memory size of 2 GB is really 2 times 1,073,741,824 (2,147,483,648 bytes). Using this information, calculate the actual number of bytes in the following

a. A memory containing 512 MB

b. A memory consisting of 512 MB words, where each word consists of 2 bytes

c. A memory consisting of 512 MB words, where each word consists of 4 bytes

d. A thumb drive that specifies 2 GB

e. A disk that specifies 4 GB

f. A disk that specifics 8 GB

Explanation / Answer

We konw that

1MB = 2 raised to the 20th power = 1048576 Bytes

1GB = 2 raised to the 30th power = 1073741824 Bytes

a)

500MB = 500 * 1048576 Bytes

number of bytes = 524288000 Bytes

b)

given 512 MB words and each word=2bytes

then

512 MB words = 500 * 1048576 * 2 bytes

number of bytes = 1048576000 Bytes

c)

given 512 MB words and each word = 4 bytes

then

512 MB words = 500 * 1048576 * 4 bytes

number of bytes = 2097152000 Bytes

d)

Given 2GB,

We know,

1GB = 2 raised to the 30th power = 1073741824 Bytes

number of bytes = 2* 1073741824 Bytes

=2147483648 Bytes

e)

Given 4GB,

We know,

1GB = 2 raised to the 30th power = 1073741824 Bytes

number of bytes = 4* 1073741824 Bytes

= 4294967296 Bytes

f)

Given 8GB,

We know,

1GB = 2 raised to the 30th power = 1073741824 Bytes

number of bytes = 8* 1073741824 Bytes

= 8589934592 Bytes

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