Write IEEE floating point representation of the following decimal number. Show your work. 1.25
1 answer:
Answer:
00111111101000000000000000000000
Explanation:
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0 01111111 01000000000000000000000
The first bit is the sign bit. It's 0 for positive numbers and 1 for negative numbers.
The next 8-bits are for the exponents.
The first 0-126₁₀ (0-2⁷⁻¹) are for the negative exponent 2⁻¹-2⁻¹²⁶.
And the last 127-256₁₀ (2⁷-2⁸) are for the positive exponents 2⁰-2¹²⁶.
You have 1.25₁₀ which is 1.010₂ in binary. But IEEE wants it in scientific notation form. So its actually 1.010₂*2⁰
The exponent bit value is 127+0=127 which is 01111111 in binary.
The last 23-bits are for the mantissa, which is the fraction part of your number. 0.25₁₀ in binary is 010₂... so your mantissa will be:
010...00000000000000000000
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