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Find the decimal equivalent of the 6-bit binary number (101.101)2
- a)5.2510
- b)5.12510
- c)5.62510
- d)6.62510
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Find the decimal equivalent of the 6-bit binary number (101.101)2a)5.2...
The decimal equivalent of the binary number 101.101 is,
= 1 x 22 + 0 x 21 + 1 x 20 + 1 x 2-1 + 0 x 2-2 + 1 × 2-3
= 4 + 0 + 1 + 0.5 + 0 + 0.125
= 5.625
= 4 + 0 + 1 + 0.5 + 0 + 0.125
= 5.625
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Community Answer
Find the decimal equivalent of the 6-bit binary number (101.101)2a)5.2...
To convert a binary number to its decimal equivalent, we need to understand the place value of each digit in the binary number. In binary representation, each digit represents a power of 2, starting from the rightmost digit with a power of 0.
Given binary number: (101.101)2
Converting the integer part:
The integer part of the binary number is 101. To convert it to decimal, we multiply each digit by the corresponding power of 2 and sum them up.
(1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 4 + 0 + 1 = 5
Converting the fractional part:
The fractional part of the binary number is 101. To convert it to decimal, we multiply each digit by the corresponding negative power of 2 and sum them up.
(1 * 2^-1) + (0 * 2^-2) + (1 * 2^-3) = 0.5 + 0 + 0.125 = 0.625
Combining the integer and fractional parts, we get the decimal equivalent of the binary number (101.101)2 as 5.62510.
Therefore, the correct answer is option 'C' (5.62510).
Given binary number: (101.101)2
Converting the integer part:
The integer part of the binary number is 101. To convert it to decimal, we multiply each digit by the corresponding power of 2 and sum them up.
(1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 4 + 0 + 1 = 5
Converting the fractional part:
The fractional part of the binary number is 101. To convert it to decimal, we multiply each digit by the corresponding negative power of 2 and sum them up.
(1 * 2^-1) + (0 * 2^-2) + (1 * 2^-3) = 0.5 + 0 + 0.125 = 0.625
Combining the integer and fractional parts, we get the decimal equivalent of the binary number (101.101)2 as 5.62510.
Therefore, the correct answer is option 'C' (5.62510).
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