Information AboutIeee 754 |
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IEEE 754 specifies four formats for representing floating-point values: single-precision (32-bit), double-precision (64-bit), single-extended precision (≥ 43-bit, not commonly used) and double-extended precision (≥ 79-bit, usually implemented with 80 bits). Only 32-bit values are required by the standard; the others are optional. Many languages specify that IEEE formats and arithmetic be implemented, although sometimes it is optional. For example, the C Programming Language , which pre-dated IEEE 754, now allows but does not require IEEE arithmetic (the C float typically is used for IEEE single-precision and double uses IEEE double-precision). The full title of the standard is IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std 754-1985), and it is also known as '''IEC 60559:1989, Binary floating-point arithmetic for microprocessor systems''' (originally the reference number was IEC 559:1989). {Link without Title} ANATOMY OF A FLOATING-POINT NUMBER Following is a description of the standards' format for floating-point numbers. Bit conventions used in this article Bit s within a Word of width W are indexed by Integer s in the range 0 to W−1 inclusive. The bit with index 0 is drawn on the right. The lowest indexed bit is usually the least significant. General layout Binary floating-point numbers are stored in a Sign-magnitude form as follows: 1 e bits f bits Width of field +-+ + -+ | ||
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