IEEE 754 Standard for Floating Point Binary Arithmetic

This computer science video describes the IEEE 754 standard for floating point binary. The layouts of single precision, double precision and quadruple precision floating point binary numbers are described, including the sign bit, the biased exponent and the mantissa. Examples of how to convert between denary (base 10) and single precision floating point binary numbers are shown, including how to round the mantissa correctly. There are also some example conversions that you can try yourself, along with their solutions. The way the exponent bias works and why this particular technique is used in the IEEE 754 standard, rather than two’s complement, is demonstrated. Some reserved exponent values are also mentioned. 0:00 Introduction 0:14 Review of fixed point binary 1:02 Review of floating point binary using two's complement 2:44 The IEEE 754 standard 4:08 Conversion from denary to single precision floating point binary 8:25 The exponent bias 13:42 Example conversions and solutions