FOCUS is a number system and supporting soft ware especially useful for microcomputer control and other signal processing applications. FOCUS has the wide ranging character of floating-point numbers with a uniformity of state distributions that give FOCUS approximately a fourfold accuracy advantage over an equal length floating-point system. FOCUS computations are typically five times faster than equal word length single precision fixed-point or integer arithmetic for a mixture of operations, comparable with hardware arithmetic in speed for many applications. Algorithms for 8-bit and two versions of 16-bit FOCUS are included. With FOCUS, an 8080A can perform the equivalent of over 20,000 18-bit floating-point additions, subtractions, multiplications, and divisions in one second, and store the results in 16-bit words. FOCUS is more than a theory, it is a completed system providing near hardware speed, 18-bit accuracy, floating-point range, and 8-bit cost.

In 1971 Kinsbury and Rayner, publishing under the title "Digital Filtering Using Logarithmic Arithmetic" [1] disclosed a sign-plus-logarithm number system, and a means of performing addition through single dimensional lookup using the formula c = b + F(a − b). The system was demonstrated on a computer. In 1975 Swartzlander and Alexopoulos disclosed Kinsbury's logarithmic arithmetic as "The Sign/Logarithm Number System" [2]. In 1977, without knowledge of prior art, we reinvented the wheel a third time, dubbing it "Focus," after the focus of resolution around the zero origin [3]. We wish now to acknowledge Kinsbury and Rayner as the pioneer authors, and also Swartzlander and Alexopoulos as prior to our publication.

This correspondence introduces a new number system, called the Focus number system which "focuses" on available resolution near zero much like an operational amplifier "focuses" on tiny deviations near virtual ground. This number system is supported by algorithms providing addition, multiplication, and higher order functions in a bare microcomputer at speeds rivaling those of existing integer arithmetic [1]-[3] performed with a costly arithmetic unit.