Question

If the IEEE Standard 754 representation of a floating point number is given as 01101110110011010100000000000000, determine the binary value represented by this 32-bit number

Answer #1

1. Identify the elements that make up the binary representation of the number:

First bit (the leftmost) indicates the sign,

1 = negative, 0 = positive.

The next 8 bits contain the exponent:

1101 1101

The last 23 bits contain the mantissa:

100 1101 0100 0000 0000 0000

2. Convert the exponent from binary (base 2) to decimal (base 10):

The exponent is allways a positive integer.

1101 1101_{(2)} =

1 × 2^{7} + 1 × 2^{6} + 0 × 2^{5} + 1 ×
2^{4} + 1 × 2^{3} + 1 × 2^{2} + 0 ×
2^{1} + 1 × 2^{0} =

128 + 64 + 0 + 16 + 8 + 4 + 0 + 1 = 221_{(10)}

3. Adjust the exponent:

Exponent adjusted = 221 - 127 = 94

4. put all the values into expression

(sign) (1 . Mantissa) × 2^{(Exponent adjusted)} =

(0) (1 . 100 1101 0100 0000 0000 0000) × 2^{94}

011001101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000

**if you have any doubt, feel free to ask in the
comments.**

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