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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)?
  • a)
    134
  • b)
    133
  • c)
    124
  • d)
    123
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
How many pulses are needed to change the contents of a 8-bit up counte...
As in a 28 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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How many pulses are needed to change the contents of a 8-bit up counte...
Solution:

To change the contents of a 8-bit up counter from 10101100 to 00100111, we need to count the number of pulses required to reach the new value.

Step 1: Convert the given values to decimal

10101100 = 172
00100111 = 39

Step 2: Calculate the difference between the two decimal values

39 - 172 = -133

Step 3: Convert the difference to binary

We need to represent -133 in 8-bit binary form using two's complement notation.

In two's complement notation, we invert all the bits and add 1 to get the negative value. So,

133 = 10000101 (binary)
Invert all the bits: 01111010
Add 1: 01111011

Therefore, the binary representation of -133 in 8-bit two's complement notation is 01111011.

Step 4: Count the number of pulses required to reach the new value

To reach the new value of 00100111, we need to count from 10101100 to 00100111, which requires counting down.

Starting from 10101100, we can count down by subtracting 1 from each value until we reach the target value of 00100111. Alternatively, we can count up by adding the two's complement representation of -133 to 10101100.

10101100 + 01111011 = 00000111

Therefore, we need 123 pulses to change the contents of the 8-bit up counter from 10101100 to 00100111. Answer is option 'D'.
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