Question

In: Computer Science

6. Assume a computer has a physical memory organized into 64-bit words. Using hexadecimal notation, give...

6. Assume a computer has a physical memory organized into 64-bit words. Using hexadecimal notation, give the word address and offset within the word for each of the following byte addresses.

Byte address

Word address

Offset

0x000b

0x03ff

0x07fc

Solutions

Expert Solution

Ans:

Given that the physical memory is organised into 64-bit words i.e. 8 bytes each.

=> Each word consists of 8 bytes.

therefore, memory will be addressed as starting from 0x0000

Since each word is of 8 byte therefore next address would be 0x0008 and then 0x0010 and next would be 0x0018 and so on.

=> In order to detemine the next word address we need to divide the byte address with 8 and use the quotient (q) as:

Word address = 0x0000 + (q*8)16

Byte address = Word address + offset

and offset will be the remainder (r) which means that in that particular word the given Byte address refers to the (r+1)th byte.

1) 0x000b = (11)10

=> 11/8 = 1 and remainder (r) = 3

quotient (q) = 1 means 2nd word in the memory.

=> Word address = 0x0008

& offset = 3 (=> address belongs to the 4th byte in this word)

2) 0x03ff = (1023)10

=> 1023/8 = 127 and remainder (r) = 7

q = 127 means 128th word in the memory.

=> Word address = 0x0000 + (127*8)16 = 0x03f8

& offset = 7 (=> address belongs to 8th byte in this word)

3) 0x07fc = (2044)10

=> 2044/8 = 2040 and r = 4

q = 2040 means 2041th word in the memory

=> Word address = 0x0000 + (2040*8)16 = 0x07f8

& offset = 4 (=>address belongs to 5th byte in this word)


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