Question

If a computer has 64-bit addresses and each address corresponds to one byte, how many gigabytes of memory can the computer address? (Show the math)

The past answers for this same question are either incorrect or do not show the math.

Answer 1

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let's suppose you have 3 bits how many numbers can you represent using these 3 bits?

1st bit 0 or 1 = 2 choices

2nd bit 0 or 1 = 2 choices

3rd bit 0 or 1 = 2 choices

so total 2*2*2 = 8 numbers

in the same way, if you have n bits then you can represent 2*2*2*.....2(n times )= 2ⁿ numbers

given each byte is represented by one 64 bit address

total bytes = total number that 64 bits can represent = 2⁶⁴

we know 2¹⁰ bytes = 1KB

2²⁰= 1 MB

2³⁰= 1GB

total memory the computer address is 2⁶⁴/ 2³⁰ GB = 2³⁴ GB