Single-precision floating-point numbers (float) and double-precision floating-point numbers (double) are the two types of floating-point numbers represented in computers, and their main differences are in precision and range.

Single-precision floating-point numbers (float) occupy 4 bytes (32 bits) in memory and have a range of values from -2^128 to 2^128, with a precision of about 7 significant digits. This type of floating-point number is suitable for use in areas such as general computing and graphics processing, but it may become insufficient when higher precision or larger ranges are required.

Double-precision floating-point numbers (double) take up 8 bytes (64 bits) in memory and have a range of values from -2^1024 to 2^1024, with a precision of about 15 effective digits. This type of floating-point number is suitable for use in areas such as scientific computing, finance, and big-data analytics because it offers higher precision and a larger range.

Overall, the main difference between single-precision floating-point numbers and double-precision floating-point numbers is precision and range. Single-precision floating-point numbers are used in areas such as general computing and graphics processing, while double-precision floating-point numbers are used in areas such as scientific computing, finance, and big-data analytics, which require higher precision and greater range.

Single-precision floating-point number complement

The complement of a number is the number that is inverted in bits (i.e., inverted) and the result is added to 1. In the complementary system, a negative number is represented by the complement of its positive counterpart.

The biggest advantage of the complementary code system is that it can be used for addition or subtraction without the need to use different calculations for positive and negative numbers. As long as a kind of addition circuit can deal with all kinds of numbered addition, and subtraction can be expressed by one number plus the complement of another number, so as long as there is an addition circuit and a complementary code circuit can complete all kinds of numbered addition and subtraction, which is quite convenient in circuit design.

In addition, there is only one way to represent 0 in the complementary code system, which is different from the inverse code system (in the inverse code system, there are two ways to represent 0), so you only need to compare the two numbers once to determine whether they are 0 or not. The table on the right shows some integers in the 8-bit complementary code system. It can be represented in the range from -128 to 127, totaling ***256 (=2) integers.

Refer to Baidu Encyclopedia-Single-Precision Floating-Point Numbers for the above