GATE IT 2005 | Question: 11

Question

How many pulses are needed to change the contents of a $8$-bit up counter from $10101100$ to $00100111$ (rightmost bit is the LSB)?

• A. $134$
• B. $133$
• C. $124$
• D. $123$

Comments

$172 \rightarrow 255 \rightarrow 0 \rightarrow 39 $ (because UP Counter)

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(rightmost bit is the LSB)

Doesn't this mean that the number is taken in reverse order? 

Answer 1

D.$123$ Pulses.

As in a $2^8$ Counter, the range would be from $0-255$. Hence to go from $10101100 (172)$ to $00100111 (39)$, the counter has to go initially from $172$ to $255$ and then from $0$ to $39$.

Hence to go from $172$ to $255,  255-172 = 83$ Clock pulses would be required. then from $255$ to $0$, again $1$ clock pulse would be required. Then, from $0$ to $39, 39$ clock pulses would be required. Hence in total $83+1+39 =123$ Clock pulses would be required.

Comments

Good

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In this 8-bit up counter, all 256 states are countable??

what if some states are not countable,I mean it counts less than 2^n states,then????

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what if some states are not countable,I mean it counts less than 2^n states,then??

@MRINMOY_HALDER  i think then we will not call it a up/down asynchronous counter.

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So, can I convience myself that all asynchronous counter contains all possible states(2^n) either up or down??

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Definitely not.

Either it is synchronous or asynchronous , if it is n bit up/down counter then it will count all possible states in specific order...

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A similar type of question

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More variation can be created using clear and preset

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@Shaik Masthan sir what happens in down counter case for the same question?

Thanks

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@halfcodeblood ans will be 133 (172-39)

Answer 2

8 bit Counter range 0-255 To go from 10101100 (172) to 00100111 (39)

• first counter will move from 172 to 255(255-172=83)
• 255 to 0=1 pulse
• and then  0 to 39(39-0=39).

Total=83+1+39=123 So answer is D  

Answer 3

1. • The counter needs to count up to $255 (11111111)$ and then back down to the target value.
   • To reach $255: 255 - 172$ (initial value) $= 83$ pulses
   • To reach the target value from $255: 39 $(target value) $- 0 = 39$ pulses
   • $1$ pulse to roll over from $255$ to $0$
   • Total pulses: $83 + 39 + 1 = 123$

Therefore, 123 pulses are needed to change the counter's contents as specified.