Floating Point Numbers

this paper. In 1985, the Institute of Electrical and Electronic Engineers published IEEE Standard 754 for floating-point arithmetic. Virtually all general purpose processors built today have floating-point units which conform to IEEE 754. The examples in this paper describe IEEE 754 floating-point number formats. Instead of using base ten and powers of ten like scientific notation, IEEE 754 floating-point uses a binary fraction and an exponent that is considered to be a power of two. The format of a single-precision floating-point number is shown in Figure 1. The leftmost bit indicates the sign of the number, with a zero indicating positive and a one indicating negative. The exponent occupies eight bits and is also signed. A negative exponent indicates that the fraction is multiplied by a negative power of two. The exponent is stored as an excess 127 number, which means that the value stored is 127 more than the true value. A stored value of one indicates a true value of-126. A stored value of 254 indicates a true value of +127. Exponents values of zero or 255 (all ones) are used for special purposes described later. The fraction part is a 23-bit binary fraction with the binary point assumed to be to the left of the first bit of the fraction. The approximate range of such a number is -- 1