Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Questions > Given the following binary number in 32-bit (...
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Given the following binary number in 32-bit (single precision) IEEE-754 format:
00111110011011010000000000000000
The decimal value closest to this floating-point number is
00111110011011010000000000000000
The decimal value closest to this floating-point number is
- a)1.45 × 101
- b)1.45 × 10-1
- c)2.27 × 10-1
- d)2.27 × 101
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Given the following binary number in 32-bit (single precision) IEEE-75...
32-bit floating-point representation of a binary number in IEEE- 754 is,
Given binary number is
00111110011011010000000000000000
Here, sign bit is 0. So, number is positive.
Exponent bits = E = 01111100 = 124 (in decimal)
Mantissa bits M = 11011010000000000000000
In IEEE-754 format, 32-bit (single precision)
(-1)s × 1.M × 2E – 127
= (-1)0 × 1.1101101 × 2124 – 127
= 1.1101101 × 2-3
= (1 + 2-1 + 2-2 + 2-4 + 2-5 + 2-7) × 2-3
= 0.231 = 2.31 × 10-1 ≈ 2.27 × 10-1
Given binary number is
00111110011011010000000000000000
Here, sign bit is 0. So, number is positive.
Exponent bits = E = 01111100 = 124 (in decimal)
Mantissa bits M = 11011010000000000000000
In IEEE-754 format, 32-bit (single precision)
(-1)s × 1.M × 2E – 127
= (-1)0 × 1.1101101 × 2124 – 127
= 1.1101101 × 2-3
= (1 + 2-1 + 2-2 + 2-4 + 2-5 + 2-7) × 2-3
= 0.231 = 2.31 × 10-1 ≈ 2.27 × 10-1
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Community Answer
Given the following binary number in 32-bit (single precision) IEEE-75...
Explanation:
Given Binary Number:
00111110011011010000000000000000
Sign Bit:
The sign bit is 0, indicating a positive number.
Exponent:
- The exponent is 01111001 in binary, which is 121 in decimal.
- To get the actual exponent value, subtract 127 from the binary exponent value: 121 - 127 = -6.
Fraction (Mantissa):
- The mantissa is 1.11011010000000000000000 in binary.
- To find the mantissa value, add an implicit leading 1 to the binary number: 1.11011010000000000000000.
- This gives us the value: 1.11011010000000000000000 = 1.861328125.
Decimal Value Calculation:
- The formula for calculating the decimal value of a floating-point number in IEEE-754 format is: (-1)^s * 1.m * 2^e.
- Substituting the values:
= (-1)^0 * 1.861328125 * 2^-6
= 1 * 1.861328125 * 2^-6
= 1.861328125 * 2^-6
= 1.861328125 * 1/64
= 1.861328125 / 64
≈ 0.029024001953125
Closest Decimal Value:
The closest decimal value to the floating-point number is approximately 0.029, which can be expressed as 2.27 x 10^-1.
Therefore, the correct answer is option C (2.27 x 10^-1).
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Given the following binary number in 32-bit (single precision) IEEE-754 format:00111110011011010000000000000000The decimal value closest to this floating-point number isa)1.45 × 101b)1.45 × 10-1c)2.27 × 10-1d)2.27 × 101Correct answer is option 'C'. Can you explain this answer?
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