5. [15 marks] An n-bit register can hold 2^n distinct bit patterns. As such, it
ID: 3784141 • Letter: 5
Question
5. [15 marks] An n-bit register can hold 2^n distinct bit patterns. As such, it can only be used to address a memory whose number of addressable units (typically, bytes) is less than or equal to 2^n. In this question, register sizes need not be a power of two. K = 2^10
a) [5 marks] What is the minimum size of an address register for a computer with 5 TB of memory? answer = _____ bits
b) [5 marks] What is the minimum size of an address register for a computer with 7 TBs of memory? answer = _____ bits
c) [5 marks] What is the minimum size of an address register for a computer with 2.5 PBs of memory? answer = _____ bits
Explanation / Answer
1)5Tb=5*2^40*8 bits
as 1tb=2^40 bytes and converting into bit means multiply by 8
2^n=5*2^40*8
solving this we get n=45.32 so our answer is 46bit
2)2^n=7*2^40*8
n=45.8 which makes our answer 46 bit
3)2^n=2.5*2^50*8
n=54.32
which gives 55bit
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