Write ieee floating point representation of the following decimal number. show your work.
1.25

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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