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Convert binary number 1101.1101 into decimal equivalent.
12.8125
13.8125
12.625
13.625
13.8125
To convert 1101.1101 to decimal, calculate the integer part 1101 as 12┬│ + 12┬▓ + 02┬╣ + 12тБ░ = 8 + 4 + 0 + 1 = 13. The fractional part.1101 is 12тБ╗┬╣ + 12тБ╗┬▓ + 02тБ╗┬│ + 12тБ╗тБ┤ = 0.5 + 0.25 + 0 + 0.0625 = 0.8125, resulting in 13.8125.
To convert 1101.1101 to decimal, calculate the integer part 1101 as 12┬│ + 12┬▓ + 02┬╣ + 12тБ░ = 8 + 4 + 0 + 1 = 13. The fractional part.1101 is 12тБ╗┬╣ + 12тБ╗┬▓ + 02тБ╗┬│ + 12тБ╗тБ┤ = 0.5 + 0.25 + 0 + 0.0625 = 0.8125, resulting in 13.8125.
The binary system is the foundational architecture of the Von Neumann model, which is the basis for most modern electronic computers developed since the 1940s.
Binary is a base-2 number system consisting only of digits 0 and 1.
The position of each digit in a binary number corresponds to a power of 2, starting from 2тБ░ for the rightmost integer digit.
Decimal conversion is performed by summing the products of each bit and its respective positional weight.
Binary arithmetic is essential for understanding data storage units like Bits, Bytes, Kilobytes, and Gigabytes.
The fractional part of a binary number is calculated using negative powers of 2 (2тБ╗┬╣ = 0.5, 2тБ╗┬▓ = 0.25, 2тБ╗┬│ = 0.125, 2тБ╗тБ┤ = 0.0625).
Option A (12.8125) is incorrect because 1101 is 13 in decimal, not 12.
Option C (12.625) is incorrect as it miscalculates both the integer and fractional binary segments.
B is correct тАФ The decimal equivalent of binary 1101.1101 is calculated as 13.8125.
Mastering number systems is vital for the 'Introduction to IT' module in competitive exams; always memorize powers of 2 up to 2┬╣тБ░ to speed up conversion calculations.
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