TRB 2006 - Question 11

 A memory system of size $16$ Kbytes is required to be designed using memory chips which have $12$ address lines and $4$ data lines each. 

The number of such chips required to design the memory system is 

a) $2$

b) $4$   

c) $8$     

d) $16$

Correct Answer: Option C

Solution:

👉Required memory size = $16$ kilobytes

As we know $1$ byte = $8$ bits and $1$ kilobytes = $1024$ bytes

Hence required memory size = $16×1024×8$ bits

👉Available memory chip has $12$ address lines and $4$ data lines, it's memory size is $2^{12}×4$ bits.

👉Required number of memory chips, $$=\frac{Required\; memory\; size}{ Available\; memory \;size}$$ $$=\frac{16×1024×8}{2^{12}×4}$$$$=\frac{2^4×2^{10}×2^3}{2^{12}×2^2}$$$$=2^{4+10+3-12-2}$$$$=2^3$$$$=8$$

We need $8$ memory chips.