**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.**

- The mantissa is a normalised negative number because the left-most bits are 10
- Write down the mantissa with the decimal point between the first two digits: 1.0010
- 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.
- The exponent is 010, which is the same as +2.
- We therefore need to move the decimal point two places to the right.
- The mantissa goes from -(0.1110) to -(011.10)
- Getting rid of redundant zeros gives us -(11.1)
- 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.**