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

  1. $134$
  2. $133$
  3. $124$
  4. $123$
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3 Answers

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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.

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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  

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    • 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.

Answer:

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