# IEEE 754 floating point number addition

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Explore the operation of the IEEE 754 floating point format, using the following steps:

(i) Explain how 32-bit (single-precision) floating-point values are stored in memory, and the function of

each bit.

(ii) Explain how two floating point numbers are added together, specifying all necessary operations on the

various parts of the operands and the result.

(iii) Illustrate your answer to parts (i) and (ii) with an example - convert the ID number 1250361 to the IEEE 754 format, as well as this number with its seven decimal digits reversed. Add these two quantities and show the

result as 32 bits in IEEE 754 format.

i.e. 1250361.0 + 1630521.0

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##### Solution Summary

IEEE 754 floating point number addition is emphasized.

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32-bit single precision IEEE 754 floating point numbers are represented in 3 parts:

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<br>1.) Sign bit: It is just 1-bit in length. If its value is 1, the number is negative. If its zero, the number is positive. It is the 31st bit if we number the bits from 0 to 31, right to left.

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<br>2.) Exponent byte: The bits 23-30 represent exponent field. It is 8 bits wide and the radix is 2, implicitly. The value 127 is added to the true exponent before storing the final exponent.

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<br>3.) Fractional field or mantissa: The rest 23 bits from 0-22 represent the fractional part. The leading '1' in normalized ...

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