A novel method for arithmetic operations using complex binary number system and the reconversion of the result to the decimal complex number system

摘要

Walter Penney defined a complex number system first by using a base of -4 and later by using (-1+j) [W. Penney, (1964), (1956)]. Other researchers have been working on the representation of complex binary numbers as one unit and perform arithmetic operations [(T.Jamil et al., (2000)]. We discuss a complex binary number system (CBNS) for high-speed arithmetic operations. An algorithm that performs the conversion of the decimal complex numbers to the binary complex number system that treats the complex number as one unit is represented [(T.Jamil (Dec2001)/Jan2002)]. A lookup table is generated to store their equivalent values in the CBNS form. We also present a new method to perform arithmetic operations (+, - , *, /) on operands in the CBNS form. A new algorithm is developed to add two complex numbers (CBNS form) using a modified carry look ahead principle. A block diagram for the adder that uses a new algorithm is presented. The results of the arithmetic operations in the CBNS form are reconverted back to the binary complex number using a new lookup table. This lookup table presents a new method for the reconversion of the CBNS numbers to the complex numbers.