Question

Suppose that a system uses 32-bit memory words and its memory is built from 16 1M × 16 RAM chips. How large, in words, is the memory on this system?

Answer 1

Answer:

Memory of the system is $2^{23}$ .

Explanation:

Computer programs are usually written in Byte. That is to say we expressing our megabyte in byte.

NOTE :  1 Megabyte  (MB)  = $2^{20}$ in Byte

Mathematically written as  :   1 MB=$2^{20}$

                                                16 MB=X

Cross multiplying the above to make X the subject of the formula.

                X = $\frac{16 x 2^{20} }{1}$  ………………i

Converting 16 to factor of two

We having  = 16 = $2^{4}$  

Therefore equation I becomes =  x =  $\frac{2^{4} x 2^{20} }{1}$

          Applying multiplication law of indices

               X =  =$2^{4}$ + $2^{20}$ =$2^{24}$  ……………………………..ii

To convert  equation ii to the number of words we divide by 2

Therefore number of words :  $\frac{2^{24} }{2}$

applying the law of indices $x^{a}$ ÷ $x^{b}$  = $x^{a-b}$

Number of words is equal to =$2^{24-1}$ = $2^{23}$

Thank you.