Question

In most microcomputers the addresses of memory locations are specified in hexadecimal. These addresses are sequential numbers that identify each memory circuit.
(a) A particular microcomputer can store an 8 bit number in each memory location. If the memory addresses range from 000016 to FF17F16, how many memory locations are there?
(b) Another microcomputer is specified to have 4096 memory locations. What range of hex addresses does this computer use?

Answer 1

Considering that the addresses of memory locations are specified in hexadecimal.

a) The number of memory locations in a memory address range ( 0000₁₆ to FFFF₁₆ )  = 65536 memory locations

b) The range of hex addresses in a microcomputer with 4096 memory locations is ;  4095

applying the given data :

a) first step : convert FFFF₁₆ to decimal           ( note F₁₆ = 15 decimal )

( F * 16^3 ) + ( F * 16^2 ) + ( F * 16^1 ) + ( F * 16^0 )

= ( 15 * 16^3 ) + ( 15 * 16^2 ) + ( 15 * 16^1 ) + ( 15 * 1 )

=  61440 + 3840 + 240 + 15 = 65535

∴ the memory locations from  0000₁₆ to FFFF₁₆ = from 0 to 65535 = 65536 locations

b) The range of hex addresses with a memory location of 4096

= 0000₁₆ to FFFF₁₆ =  0 to 4096

∴ the range = 4095

Hence we can conclude that the memory locations in ( a ) = 65536 while the range of hex addresses with a memory location of 4096 = 4095.

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