GATE IT 2005 | Question: 9

Question

A dynamic RAM has a memory cycle time of $64$ $\text{nsec}$. It has to be refreshed $100$ times per msec and each refresh takes $100$ $\text{nsec}$ . What percentage of the memory cycle time is used for refreshing?

• A. $10$
• B. $6.4$
• C. $1$
• D. $0.64$

Comments

1 ms = 10⁶ ns
In 10⁶ ns refresh 100 times
Each refresh takes 100 ns
Memory cycle time = 64 ns.
Refresh time per 1 ms i.e per 10⁶ ns = 100*100 = 10⁴ ns
Refresh time per 1 ns = $\Large\frac{10^{4}}{10^{6}}$ ns
Refresh time per cycle = $\Large\frac{10^{4}* 64}{10^{6}}$ = .64 ns
Percentage of the memory cycle time is used for refreshing =  $\Large\frac{.64*100}{64}$ = 1%

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Hope, this is the simplest solution:

m/m cycle time = $64 ns$
In $1 ms = 10^6 ns$
Total number of memory cycles in 1 ms = $\frac{10^6ns}{64ns} = \frac{10^6}{64} $ Cycles.

Total time spent in refresh operation per millisecond $= 100*100ns = 10^4ns$

Total number of memory cycles in refresh operation per millisecond $= \frac{10^4ns}{64ns} = \frac{10^4}{64}$ cycles.

% of the memory cycle time used for refreshing = $\frac{\text{memory cycles spent in refresh operation}}{\text{total m/m cycles}}$

$=\frac{\frac{10^4}{64}}{\frac{10^6}{64}} = \frac{10^4}{10^6} = \frac{1}{100} = 0.01 = 1$%

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So basically, 100 refreshes every msec

= $10^5$ refreshes every sec

= $10^7$ ns of refreshing every sec

= $10^7$ ns of refreshing every $10^9$ ns

= $1$ in $100$ time spent refreshing, regardless of whether the memory was being used or not.

If it is being used, 1% of the memory cycle time must be used for refreshing.

If it is idle, it has to spend 1% of the idle time in refreshing.

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Given m/m cycle time=64ns

Given ,DRAM needs to be refreshed 100 times per ms

& each refresh takes 100ns

now % of mem cycle used for refreshing .

above is given data read it carefully

solution=
 
In every 1ms= DRAM refreshed 100 times

therefore, 10^6ns= DRAM refreshed 100 times

similiarly, 1ns= DRAM refreshed (100/10^6) times

so, (1m/m cycle) ,64ns= DRAM refreshed (100/10^6)*64 times ,which is turned out to be 64*10^(-4)

so we can conclude that in one mem cycle DRAM is refreshed 64*10^(-4) times

now, given one refresh takes 100ns

therefore, (64*10^(-4)) refreshes takes = (64*10^(-4))*100ns

which is turned out to be 64*10^(-2) ns ,that can be written as 0.64ns

basically, question is asking in one mem cycle that is 64ns,how much time is used for refreshing which is 0.64ns

in terms of percentage=(0.64/64)*100%
                                         =1%
hope this helps,any corrections and suggestions please let me know.

Answer 1

Ans :  (C) $1$

In $1\text{ ms}$ refresh $100$ times

In $64\text{ ns}$ – refresh $\dfrac{100}{10^{-3}} \times 64 \times 10^{-9}$ times

$\quad=10^5 \times 10^{-9} \times 64 = 64 \times 10^{-4} $ times

In $1$ memory cycle, refresh $64 \times 10^{-4}$ times

$1$ refresh takes $100\text{ ns}$

$64 \times 10^{-4} \text{ refreshes take } 100 \times 10^{-9} \times 64 \times 10^{-4}$

$\qquad =64 \times 10^{-11}\text{ s}$

$\therefore \% \text{ refreshing time} =\frac{\text{refreshing time in cycle}}{\text{total time}} \times 100$

$\require{cancel}\qquad =\frac{\cancel{64} \times 10^{-11}}{\cancel{64} \times 10^{-9}} \times 100$

$\require{cancel}\qquad =\frac{1}{\cancel {10^2}} \times \cancel{100} = 1\%$

Comments

how did you cut the 100. can you teach me Latex?

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$\cancel {100}$

wow

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Answer will be independent of the value of memory cycle time. We can try using value $x$ instead of $64$ and try to derive it.

Other way of doing it could be to calculate the fraction of time we are doing refresh which will again come out to be $1\%$.

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DRAM works by representing the presence of data bits as charge in a capacitor. The capacitor gradually discharges over time. Therefore, to prevent data loss, it is important to refresh the data.

source

Answer 2

Time for refresh = 100ns

Number of refreshes in a memory cycle = 100 * memory cycle time/ 1ms
= 100 * 64ns/1ms = 6.4 * 10^-3

So, time for refresh in a memory cycle = 100 ns * 6.4 * 10^-3
= 64 * 10^-2 ns 

So, percentage of time spent for refresh = (64 * 10^-2 / 64) *100 = 1%

Comments

How can number of refreshes be 6.4 * 10-3 shouldn't this be an integer like 1 time or 2 time?

Answer 3

100 refreshes in 1 msec

$100\times 100 nsec$ (time tken in refreshing) in  $1 msec \text{ or } 10^6nsec.$

$\implies 1 ns$ time is taken for refresh , out of every $100 nsec$.

$\Rightarrow$  1%

Answer 4

Memory cycle time: Time between any two consecutive memory operations. Here it is given as 64 nanosecond.

The questions says “Dynamic ram” which implys that the the memory unit needs to be refreshed constantly to maintain its state, otherwise it will loose its contents. But how fast we need to refresh it, it is also given as “100 times per millisecond”.

converting everything to nanosecond:

→ In 1 millisec we do 100 refreshes

→ In $10^{6}$ nanosec we do 100 refreshes. (1 millisec = $10^{6}$nanosec)

→ In 1 nanosec we do $\frac{100}{10^{6}}$ refreshes (0.0001 refreshes)

So in 64 nanosec we do 0.0001 * 64 = 0.0064 refreshes.

This means that out of our 64 nanosec memory cycle time 0.0064 nanosec is spend only on refresh operation, the ques asks this value only, but in percentages.

$\frac{0.0064}{64}*100=1$%

 

Comments

(0.0064/64)*100 gives 0.01 not 1%.

Each refresh takes 100ns, you forgot to multiply that, then answer will come 1%.