Tutorial: Floating-point arithmetic on FPGAs

By Geir Kjosavik, Xilinx
December 13, 2006 -- dspdesignline.com

This article explains the basics of floating-point arithmetic, how floating-point units (FPUs) work, and how to use FPGAs for easy, low-cost floating-point processing.

Inside microprocessors, numbers are represented as integers—one or several bytes stringed together. A four-byte value comprising 32 bits can hold a relatively large range of numbers: 232, to be specific. The 32 bits can represent the numbers 0 to 4,294,967,295 or, alternatively, -2,147,483,648 to +2,147,483,647. A 32-bit processor is architected such that basic arithmetic operations on 32-bit integer numbers can be completed in just a few clock cycles, and with some performance overhead a 32-bit CPU can also support operations on 64-bit numbers. The largest value that can be represented by 64 bits is really astronomical: 18,446,744,073,709,551,615. In fact, if a Pentium processor could count 64-bit values at a frequency of 2.4 GHz, it would take it 243 years to count from zero to the maximum 64-bit integer.

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