What is precision?
It refers to how closely a binary floating point representation can represent a real value. Real values have infinite precision and infinite range. Digital values have finite range and precision. In practice a single-precision IEEE-754 can represent real values of a precision of 6 significant figures (decimal), while double-precision is good for 15 significant figures.
The practical effect of this for example is that a single precision value: 123456000.00 cannot be distinguished from say 123456001.00, but equally a value 0.00123456 can be represented.
What is it used for?
Precision is not used for anything other than to define a characteristic of a particular floating point representation.
What is mantissa and what is mantissa used for?
The term is not mentioned in the English language Wikipedia article, and is imprecise – in mathematics in general it has a different meaning that that used here.
The correct term is significand. For a decimal value 0.00123456 for example the significand is is 123456. 123456000.00 has exactly the same significand. Each of these values has the same significand but a different exponent. The exponent is a scaling factor which determines where the decimal point is (hence floating point).
Of course IEEE754 is a binary floating point representation not decimal, but for the same of explanation of the terms it is perhaps easier to use decimal.
How to determine the range of float/double by their size?
By the size alone you cannot; you need to know how many bits are assigned to the significand and how many bits are assigned to the exponent. In C however the range is defined by the macros FLT_MIN, FLT_MAX, DBL_MIN and DBL_MAX in the float.h header. Other characteristics of the implementations floating point representation are described there also.
Note that a specific compiler may not in fact use IEEE754, however that is the format used by most hardware FPU implementations, and the compiler will naturally follow that. For targets with no FPU (small embedded processors typically), other formats may be used.
What is ± symbol (Plus-minus) used for?
It simply means that the value given may be both positive or negative. It may refer to a specific value, or it may indicate a range. So ±n may refer to two discrete values -n or +n, or it may mean a range -n to +n. Context is everything! In this article it refers to discrete values +0, -0, +∞ and -∞.
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solved Problematic understanding of IEEE 754 [closed]