Книга: Introduction to Microprocessors and Microcontrollers

Size, accuracy and speed

The mantissa can go as high as 1.1111 1111 1111 1111 1111 111₂. To the right of the binary point the decimal equivalents are values of 1.5+0.25+0.125+0.0625 etc. Adding these up gives a total that is virtually 2 – but not quite. The larger the number of bits in the mantissa, the more accuracy we can expect in the result. The exponent has eight bits so it can range from –127 to +128 giving a maximum number of 1?2¹²⁸ which is approximately 3.4?10³⁸. The accuracy is limited by the number of bits that can be stored in the mantissa, which in this case is 23 bits.

If we want to keep to a total of 32 bits, then we have a trade-off to consider. Any increase in the size of the exponent, to give us larger numbers, must be matched by reducing the number of bits in the mantissa that would have the effect of reducing the accuracy. Floating point operations per second (FLOPS) is one of the choices for measuring speed.

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