New Fixed-Point Math for Logic Design

This book presents a new math approach for logic designs using fixed-point decimal and binary calculations. Problems resulting from rounding off and 2's complement operations are avoided. In computers, calculations are executed with fixed-point and floating-point binary numbers. The floating-point numbers have an advantage over fixed-point numbers. They are implemented with signed magnitude binary numbers and have an almost infinity range of positive and negative values. They are symmetrical with respect to integer zero. On the other hand, beside their limited range, fixed-point binary numbers are well suited for logic circuit implementation. But the binary fixed-point numbers and integers are not symmetrical with respect to integer zero. The need to compute 2's complement values results into extra work and gate count. The solution is to apply averaging and symmetry to fixed-point numbers. In 3D graphics, averaging makes for better solutions by removing many problems and corner cases.