Floating Point Numbers

Click any bit to toggle it between 0 and 1.

Normalisation (storing only one digit before the point) ensures each value has a unique representation, maximises precision by using all mantissa bits, and makes comparing numbers straightforward. A normalised number's mantissa starts with 01 or 10.

Format used here: both the mantissa and exponent use two's complement, which is the format required by AQA. The value of the number is mantissa × 2^exponent, where the mantissa is treated as a two's complement binary fraction (bit 0 has weight −1, bit 1 has weight 2⁻¹, and so on).
Zero is a special case: it is stored as all mantissa and exponent bits set to 0. This is the one value that cannot be normalised — and that is accepted convention rather than an error.