### Abstract

At the IEEE SoutheastCon 2000 held at Nashville, Tennessee, a research paper entitled "Towards implementation of a binary number system for complex numbers" presented at the conference had started my journey in pursuit of equal opportunity representation for complex numbers in the realm of computing. Given that these numbers play an important role in engineering applications such as digital signal processing and image processing, one would assume that they are treated with much respect in computer science and engineering but, alas, it was found that, instead of treating them as a dignified pair of real and imaginary components, a villainous "divide-and-conquer" technique is used in computer arithmetic to deal with these numbers. In this treatment of complex numbers, a complex number is broken-up into its real and imaginary parts and then operations are carried out on each part as if it was a part of the real arithmetic. At the end, the overall result of the complex operation is obtained by the accumulation of the individual results. In other words, addition of two complex numbers requires two separate additions (one for the real parts and one for the imaginary parts) while multiplication of the same two complex numbers requires four individual multiplications, one subtraction, and one overall addition. This can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as single unit instead of two sub-units of real and imaginary components.

Original language | English |
---|---|

Title of host publication | SoutheastCon 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Volume | 2016-July |

ISBN (Electronic) | 9781509022465 |

DOIs | |

Publication status | Published - Jul 7 2016 |

Event | SoutheastCon 2016 - Norfolk, United States Duration: Mar 30 2016 → Apr 3 2016 |

### Other

Other | SoutheastCon 2016 |
---|---|

Country | United States |

City | Norfolk |

Period | 3/30/16 → 4/3/16 |

### Fingerprint

### Keywords

- binary number
- complex binary number
- complex number
- computer arithmetic

### ASJC Scopus subject areas

- Computer Networks and Communications
- Software
- Electrical and Electronic Engineering
- Control and Systems Engineering
- Signal Processing

### Cite this

*SoutheastCon 2016*(Vol. 2016-July). [7506735] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SECON.2016.7506735

**Complex Binary Number System.** / Jamil, Tariq.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*SoutheastCon 2016.*vol. 2016-July, 7506735, Institute of Electrical and Electronics Engineers Inc., SoutheastCon 2016, Norfolk, United States, 3/30/16. https://doi.org/10.1109/SECON.2016.7506735

}

TY - GEN

T1 - Complex Binary Number System

AU - Jamil, Tariq

PY - 2016/7/7

Y1 - 2016/7/7

N2 - At the IEEE SoutheastCon 2000 held at Nashville, Tennessee, a research paper entitled "Towards implementation of a binary number system for complex numbers" presented at the conference had started my journey in pursuit of equal opportunity representation for complex numbers in the realm of computing. Given that these numbers play an important role in engineering applications such as digital signal processing and image processing, one would assume that they are treated with much respect in computer science and engineering but, alas, it was found that, instead of treating them as a dignified pair of real and imaginary components, a villainous "divide-and-conquer" technique is used in computer arithmetic to deal with these numbers. In this treatment of complex numbers, a complex number is broken-up into its real and imaginary parts and then operations are carried out on each part as if it was a part of the real arithmetic. At the end, the overall result of the complex operation is obtained by the accumulation of the individual results. In other words, addition of two complex numbers requires two separate additions (one for the real parts and one for the imaginary parts) while multiplication of the same two complex numbers requires four individual multiplications, one subtraction, and one overall addition. This can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as single unit instead of two sub-units of real and imaginary components.

AB - At the IEEE SoutheastCon 2000 held at Nashville, Tennessee, a research paper entitled "Towards implementation of a binary number system for complex numbers" presented at the conference had started my journey in pursuit of equal opportunity representation for complex numbers in the realm of computing. Given that these numbers play an important role in engineering applications such as digital signal processing and image processing, one would assume that they are treated with much respect in computer science and engineering but, alas, it was found that, instead of treating them as a dignified pair of real and imaginary components, a villainous "divide-and-conquer" technique is used in computer arithmetic to deal with these numbers. In this treatment of complex numbers, a complex number is broken-up into its real and imaginary parts and then operations are carried out on each part as if it was a part of the real arithmetic. At the end, the overall result of the complex operation is obtained by the accumulation of the individual results. In other words, addition of two complex numbers requires two separate additions (one for the real parts and one for the imaginary parts) while multiplication of the same two complex numbers requires four individual multiplications, one subtraction, and one overall addition. This can be effectively reduced to just one complex addition or only one multiplication and addition respectively for the given cases if each complex number is represented as single unit instead of two sub-units of real and imaginary components.

KW - binary number

KW - complex binary number

KW - complex number

KW - computer arithmetic

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U2 - 10.1109/SECON.2016.7506735

DO - 10.1109/SECON.2016.7506735

M3 - Conference contribution

VL - 2016-July

BT - SoutheastCon 2016

PB - Institute of Electrical and Electronics Engineers Inc.

ER -