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Q. What do you mean by Mantissa?
The mantissa, as well known as the significand, represents the precision bits of the number. It is composed of an implied leading bit and the fraction bits.
To discover the value of the implicit leading bit, consider that any number can be expressed in scientific notation in many different ways. For illustration, the number five can be represented as any of these:
5.00 × 100
0.05 × 102
5000 × 10-3
In order to increase the quantity of representable numbers, floating-point numbers are usually stored in normalized form. This essentially puts the radix point after the first non-zero digit. In standardize form five is represented as 5.0 × 100.
A nice little optimization is accessible to us in base two, since the only possible non-zero digit is 1. Therefore, we can just assume a leading digit of 1, and don't need to represent it explicitly. Since a result, the mantissa has effectively 24 bits of resolution, by way of 23 fraction bits.
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example
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