The size of RAM available is specified to be 64 Gigabytes Re

The size of RAM available is specified to be 64 Gigabytes. Recall that one byte is the collection of 8 bits, one word contains 16 bits, and a double word is given by 32 bits. Use powers of two to derive the storage capacity of memory: In terms of the total number of directly addressable bytes. In terms of the total number of directly addressable words, and in terms of directly addressable double words.

Solution

1 Byte = 8 bit = 2³ bit

1 Kilobytes = 1024 Bytes = 2¹⁰ Bytes

1 Megabytes = 1024 Kilobytes = 2¹⁰ Kilobytes

1 Gigabytes = 1024 Megabytes = 2¹⁰ Megabytes

So,

Answer (a):

64 Gigabytes = 2⁶ Gigabytes

= 2⁶ x 2¹⁰ Megabytes

= 2⁶ x 2¹⁰ x 2¹⁰ Kilobytes

= 2⁶ x 2¹⁰ x 2¹⁰ x 2¹⁰ Bytes

= 2³⁶ Bytes

Hence total number of directly addresable Bytes = 2³⁶ Bytes

Answer (b):

64 Gigabytes = 2³⁶ Bytes // Comment: (As derived in Answer (a))

64 Gigabytes = 2³⁶ x 2³ bit // Comment: (Because of the fact 1 Byte = 8 bit = 2³ bit)

64 Gigabytes = 2³⁹ bit.

Total number of directly addresable bits = 2³⁹ bit.

1 Word contains 16 bits.

1 Word contains 2⁴ bits. (In terms of power of 2)

So total number of directly addressable words = Total number of directly addresable bits / bits a word contains

= 2³⁹ / 2⁴

= 2^(39-4)

= 2⁽³⁵⁾ words.

Answer (c):

64 Gigabytes = 2³⁶ Bytes // Comment: (As derived in Answer (a))

64 Gigabytes = 2³⁶ x 2³ bit // Comment: (Because of the fact 1 Byte = 8 bit = 2³ bit)

64 Gigabytes = 2³⁹ bit.

Total number of directly addresable bits = 2³⁹ bit.

A Double Word contains 32 bits.

A Double Word contains 2⁵ bits. (In terms of power of 2)

So total number of directly addressable double words = Total number of directly addresable bits / bits a double word contains

= 2³⁹ / 2⁵

= 2^(39-5)

  = 2⁽³⁴⁾ words.