5 15 marks An nbit register can hold 2n distinct bit pattern

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

Solution

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