New Fixed-Point Math for Logic Design

This book presents a new math approach for binary calculations in logic designs using fixed-point decimal numbers. In computers, calculations are executed with fixed-point and floating-point binary numbers. The floating-point numbers have an advantage because of their almost infinite range of positive and negative values. They are implemented with signed magnitude binary numbers and are symmetrical with respect to integer zero. On the other hand, beside of their limited range, fixed-point binary numbers are well suited for most logic design implementations. But the binary fixed-point numbers and integers are not symmetrical with respect to integer zero. The solution is to apply averaging and symmetry to fixed-point numbers. With ""averaging"", problems resulting from rounding off and 2's complement operations are avoided. These techniques have resulted in more efficient designs with lower gate count and lower cost.