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A single-precision floating point number contains the sequence of bits 100011111 00000000001 000000000000, Information is stored in the following left-to-right order, sign bit, exponent (bias 127) and mantissa. Which of the following representation in decimal is equivalent?
  • a)
    231 (1 + 2-12)
  • b)
    (-1) 231(1 + 2-12)
  • c)
    (—1) 2-65 (1 + 2-10)
  • d)
    (-1) 2-96 (1 + 2-11)
Correct answer is option 'D'. Can you explain this answer?
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A single-precision floating point number contains the sequence of bits...
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A single-precision floating point number contains the sequence of bits...
The given sequence of bits can be divided into three parts: sign bit, exponent, and mantissa.

Sign bit: 1 (since the leftmost bit is 1, signifying a negative number)

Exponent: 00011111 (bias 127)
Converting the exponent to decimal:
00011111 = 31 (in binary)
31 - 127 = -96 (after subtracting the bias)

Mantissa: 00000000001

Putting all the parts together, the number can be represented as:
(-1)^1 * 2^(-96) * 1.00000000001

So the equivalent representation in decimal is:
(-1) * 2^(-96) * 1.00000000001

Therefore, the correct answer is:
b) (-1) * 2^31 * (2^-12)
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A single-precision floating point number contains the sequence of bits 100011111 00000000001 000000000000, Information is stored in the following left-to-right order, sign bit, exponent (bias 127) and mantissa.Which of the following representation in decimal is equivalent?a)231 (1 + 2-12)b)(-1) 231(1 + 2-12)c)(—1) 2-65 (1 + 2-10)d)(-1) 2-96 (1 + 2-11)Correct answer is option 'D'. Can you explain this answer?
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