Question:
What is the decimal equivalent of the IEEE 754 single-precision floating point representation:
0 10000001 10100000000000000000000?
IEEE 754 सिंगल-प्रिसिजन फ्लोटिंग पॉइंट प्रतिनिधित्व
0 10000001 10100000000000000000000 का दशमलव मान क्या है?
Options:
- 6.5
- 3.25
- 13.0
- 1.625
- 6.5
- 3.25
- 13.0
- 1.625
Correct Answer: a)
Explanation:
1. Sign bit \(S = 0\) (positive).
2. Biased Exponent \(E = 10000001_2 = 129\). Actual exponent \(e = 129 – 127 = 2\).
3. Mantissa fraction \(M = 1010…_2 = 1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = 0.5 + 0.125 = 0.625\).
Value = \((-1)^0 \times (1 + M) \times 2^e = 1 \times 1.625 \times 2^2 = 1.625 \times 4 = 6.5\).
2. Biased Exponent \(E = 10000001_2 = 129\). Actual exponent \(e = 129 – 127 = 2\).
3. Mantissa fraction \(M = 1010…_2 = 1 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = 0.5 + 0.125 = 0.625\).
Value = \((-1)^0 \times (1 + M) \times 2^e = 1 \times 1.625 \times 2^2 = 1.625 \times 4 = 6.5\).
साइन बिट 0 (धनात्मक), एक्सपोनेंट = \(129 – 127 = 2\)। मेंटिसा = \(1 + 0.5 + 0.125 = 1.625\)। मान = \(1.625 \times 2^2 = 6.5\)।