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Negative floating point numbers using one byte 

Negative binary floating-point number representation using one byte
Now let's look at some negative numbers. These are some more steps in dealing with negative numbers than in dealing with positive numbers but it is still a mechanical process. Work through the following examples carefully, taking note of each step.

Remember! A normalised negative binary floating-point number always begins 10

Example 16. Convert 10010010 (using 5 bits for the mantissa and 3 for the exponent) into decimal.

    1. The mantissa is a normalised negative number because the left-most bits are 10
    2. Write down the mantissa with the decimal point between the first two digits: 1.0010
    3. Because it’s negative, there is an extra step. You must convert it into a negative binary number that is not in 2s complement form. 1.0010 therefore becomes -(0.1110) Notice that the decimal place stays where it is for the moment. If you are having trouble with this step, refer back to the ‘Getting back to a negative denary number’ section.
    4. The exponent is 010, which is the same as +2.
    5. We therefore need to move the decimal point two places to the right.
    6. The mantissa goes from -(0.1110) to -(011.10)
    7. Getting rid of redundant zeros gives us -(11.1)
    8. Converting this fixed-point number gives us -(3.5) or simply -3.5

Example 17. Convert 10111110 (using 5 bits for the mantissa and 3 for the exponent) into decimal.

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