Floating point

In Computer Science the term floating point refers to a kind of number, that can be stored, in computer memory, and which can have arithmetic operations performed on it.

Computer Scientist contrast floating point numbers with "fixed point numbers", also called "integers", which have no fractional component. Computer integers are a subset of true mathematical integers, limited by the number of computer bits set aside for them. When the sum of two fixed point numbers exceeds the number of bits set aside to hold a fixed point number, it is truncated. When one fixed point number is divided by another, and the results would have a fractional component, the fractional component is discarded.

Floating point numbers are also limited by the number of computer bits set aside for them, but can hold much larger and much smaller numbers, because each floating point number contains two values, an exponent which specifies the size of the number, and a mantissa, which records the leading digits of the number.

Computer's central processing unit's are able to perform the arithmetic operations of addition, subtraction, multiplication and division, when one number is a fixed point number and the other is a floating point number.

The IEEE specified industry standards for how computer manufacturers should handle floating point numbers -- IEEE 754 Single-Precision Floating-Point Format. According to IEEE 754 standard the largest number that can be stored in 32 bits is approximately 3.4029235 times 10 to the 38th power. Floating point numbers that use 64 bits can store up to 1.79 times 10 to the 308th power. 1.18 times 10 to the 4932 power is the largest number that can be stored in 128 bits. The smallest 32, 64 and 128 bit values are 1.17549435 times 10 to the minus 38 power, 4.94 times 10 to the minus 324 power and 6.47 times 10 to the minus 4966.