Decimal-Binary Conversions in CORDIC

Abstract

A special-purpose, binary computer called CORDIC (COordinate Rotation DIgital Computer) contains a unique arithmetic unit composed of three shift registers, three adder-subtractors, and suitable interconnections for efficiently performing calculations involving trigonometric functions. A technique is formulated for using the CORDIC arithmetic unit to convert between angles expressed in degrees and minutes in the 8, 4, 2, 1 code and angles expressed in binary fractions of a half revolution. Decimal-to-binary conversion is accomplished through the generation of an intermediate binary code in which the variable values are +1 and -1. Each of these intermediate code variables controls the addition or subtraction of a particular binary constant in the formation of an accumulated sum which represents the angle. Examples are presented to illustrate the technique. Binary-to-decimal conversion is accomplished by applying essentially the same conversion steps in reverse order, but this feature is not discussed fully. Fundamental principles of the conversion technique, rather than details of implementation, are emphasized. The CORDIC conversion technique is sufficiently general to be applied to decimal-binary conversion problems involving other mixed radix systems and other decimal codes.