How many numbers of double data are reserved by default in C language?

Double type data in C language retains 15 decimal places by default. It uses the IEEE 754 standard to represent floating point numbers, where the mantissa uses a 52-bit binary number and can represent 2^52 different values. However, due to exponent bias, 15 decimal places are actually retained.

Double type data in C language retains several decimal places by default

Double type data is used in C language Built-in data type for storing double-precision floating-point numbers. It retains 15 decimal places by default.

The principle of retaining decimals

Floating point numbers in C language are represented using the IEEE 754 standard. This standard defines the binary representation of floating point numbers, which includes:

• Mantissa: represents the decimal part, using normalized binary representation.
• Exponent: indicates the position of the decimal point, expressed using a biased exponent.
• Sign bit: Indicates the sign (positive or negative) of the floating point number.

Double type data uses 64-bit binary to store floating point numbers, where:

• 1 bit: Sign bit
• 11 digits: Exponent
• 52 digits:Mantissa

##Calculation of decimal places

The mantissa is a 52-bit long binary number that can represent 2^52 = 4,503,599,627,370,496 different values. In the representation of floating point numbers, the actual value represented by the mantissa is:

<code>实际值 = 尾数 * 2^指数</code>

Therefore, for double type data, because it retains a 52-bit mantissa, it can represent 2^52 different mantissas, This means that it can retain 52 decimal places. However, due to the offset of the exponent, double data actually retains 15 decimal places by default.

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