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Question Id : 4377 | Context :NIMCET 2017

Question

The representation of a floating point binary number +1001.11 in 8 bit fraction and 6 bit exponent format is
🎥 Video solution / Text Solution of this question is given below:

✅ Given:

The floating-point binary number is +1001.112.

We need to convert it into an 8-bit fraction and a 6-bit exponent format.

✅ Step 1: Normalize the Binary Number

We start by normalizing the binary number into scientific notation of the form:

1.xxxx×2n

Converting 1001.112 into scientific notation gives:

1001.112=1.001112×23

The exponent is 3 (because the binary point is shifted 3 places to the left).

✅ Step 2: Convert the Exponent to Binary

The exponent is 3 in decimal. To represent this in binary using 6 bits, we get:

Exponent=0001002

✅ Step 3: Convert the Fraction to 8 Bits

The fractional part of the normalized binary number is 00111. We need to extend it to 8 bits:

Fraction=010011102

✅ Final Answer:

The floating-point binary number +1001.112 in 8-bit fraction and 6-bit exponent format is:

Exponent: 0001002, Fraction: 010011102

📲


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Ask Your Question or Put Your Review.
Manmohan dwivedi-pic
Manmohan dwivedi , Nimcet
Commented May 21 , 2022
Since +1001.11 is positive the sign bit = 1 (1001.11)2 = (0.100111) × 24 = (0.10011100) × 24 Fraction : (1001110)2 = (01001110)2 Exponent = (4)10 = (100)2 = (000100)2 1 is correct
Suraj kumar agarwal-pic
Suraj kumar agarwal , Mca aspirants
Commented Oct 08 , 2020
anyone please explain this