Question

A processor can support a maximum memory of 4 GB, where the memory is word-addressable (a word consists of two bytes). The size of the address bus of the processor is at least_______ bits. 

Answer 1

Maximum memory size = 4 GB = 2³² bytes

Word size = 2 byte

Total number of words = \(\frac{{memory\;size}}{{word\;size}} = \;\frac{{{2^{32}}}}{2} = {2^{31}}\)

To, address these words, minimum size of the address bus we needed = 2³¹

Minimum size of address bus in bits = \(\left\lceil {{{\log }_2}{2^{31}}} \right\rceil \) = 31 bits

NOTE:

1 G → 2³⁰