'float' vs. 'double' precision

Floating point numbers in C use IEEE 754 encoding.

This type of encoding uses a sign, a significand, and an exponent.

Because of this encoding, many numbers will have small changes to allow them to be stored.

Also, the number of significant digits can change slightly since it is a binary representation, not a decimal one.

Single precision (float) gives you 23 bits of significand, 8 bits of exponent, and 1 sign bit.

Double precision (double) gives you 52 bits of significand, 11 bits of exponent, and 1 sign bit.

Do doubles always have 16 significant figures while floats always have 7 significant figures?

No. Doubles always have 53 significant bits and floats always have 24 significant bits (except for denormals, infinities, and NaN values, but those are subjects for a different question). These are binary formats, and you can only speak clearly about the precision of their representations in terms of binary digits (bits).

This is analogous to the question of how many digits can be stored in a binary integer: an unsigned 32 bit integer can store integers with up to 32 bits, which doesn't precisely map to any number of decimal digits: all integers of up to 9 decimal digits can be stored, but a lot of 10-digit numbers can be stored as well.

Why don't doubles have 14 significant figures?

The encoding of a double uses 64 bits (1 bit for the sign, 11 bits for the exponent, 52 explicit significant bits and one implicit bit), which is double the number of bits used to represent a float (32 bits).

• float: 23 bits of significand, 8 bits of exponent, and 1 sign bit.
• double: 52 bits of significand, 11 bits of exponent, and 1 sign bit.