onvert (67.250) 10 to Binary*
Question
onvert (67.250) 10 to Binary*
Solution
To convert the decimal number 67.250 to binary, we need to handle the integer part (67) and the fractional part (0.250) separately.
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Convert the integer part:
Start by dividing the number by 2 and record the remainder. Continue this process, dividing the result (ignoring the remainder) by 2 each time and recording the remainder, until the result is 0.
67 / 2 = 33 remainder 1 (least significant bit or LSB) 33 / 2 = 16 remainder 1 16 / 2 = 8 remainder 0 8 / 2 = 4 remainder 0 4 / 2 = 2 remainder 0 2 / 2 = 1 remainder 0 1 / 2 = 0 remainder 1 (most significant bit or MSB)
Reading the remainders from bottom to top gives the binary equivalent of the integer part: 1000011.
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Convert the fractional part:
Multiply the fractional part by 2, record the whole number part, and then continue the process with the fractional part of the result, until the fractional part is 0 or you have enough precision.
0.250 * 2 = 0.500 (whole number part is 0) 0.500 * 2 = 1.000 (whole number part is 1)
Reading the whole number parts from top to bottom gives the binary equivalent of the fractional part: 01.
So, the binary equivalent of the decimal number 67.250 is 1000011.01.
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