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Previous Year Question (PYQs)

The number X is given in IEEE 32-bit floating point format. What is the equivalent decimal value? $X = 1\ 10000011\ 11101100000000000000000$




Solution

Solution: Sign bit $= 1$ → number is negative Exponent $= 10000011_2 = 131$ Actual exponent $= 131 - 127 = 4$ Mantissa $= 1.111011_2$ $= 1 + \frac12 + \frac14 + \frac18 + \frac1{64}$ $= 8.1640625$ Value $= -(8.1640625 \times 2^4)$ $= -130.625$

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