### Abstract

Complex numbers play an important role in engineering applications such as digital signal processing and image processing. To represent these numbers in binary, a 'divide-and-conquer'' technique is used in today's computer systems wherein 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, (a+jb) and (c+ jd), requires two separate additions, (a+c) and (b+d), while multiplication of the same two complex numbers requires four individual multiplications (ac., ad., bc., bd), one subtraction (ac-bd) =x, one addition (ad+bc)= y, and one overall addition x+jy. 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. This paper highlights the research on (-1+j)-based binary number system, called Complex Binary Number System (CBNS), as it was presented in a tutorial at the IEEE SoutheastCon 2018.

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

Title of host publication | Southeastcon 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Volume | 2018-April |

ISBN (Electronic) | 9781538661338 |

DOIs | |

Publication status | Published - Oct 1 2018 |

Event | 2018 IEEE Southeastcon, Southeastcon 2018 - St. Petersburg, United States Duration: Apr 19 2018 → Apr 22 2018 |

### Other

Other | 2018 IEEE Southeastcon, Southeastcon 2018 |
---|---|

Country | United States |

City | St. Petersburg |

Period | 4/19/18 → 4/22/18 |

### Fingerprint

### Keywords

- associative dataflow
- associative memory
- 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 2018*(Vol. 2018-April). [8478931] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SECON.2018.8478931

**Complex Binary Associative Dataflow Processor - A Tutorial.** / Jamil, Tariq.

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

*Southeastcon 2018.*vol. 2018-April, 8478931, Institute of Electrical and Electronics Engineers Inc., 2018 IEEE Southeastcon, Southeastcon 2018, St. Petersburg, United States, 4/19/18. https://doi.org/10.1109/SECON.2018.8478931

}

TY - GEN

T1 - Complex Binary Associative Dataflow Processor - A Tutorial

AU - Jamil, Tariq

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Complex numbers play an important role in engineering applications such as digital signal processing and image processing. To represent these numbers in binary, a 'divide-and-conquer'' technique is used in today's computer systems wherein 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, (a+jb) and (c+ jd), requires two separate additions, (a+c) and (b+d), while multiplication of the same two complex numbers requires four individual multiplications (ac., ad., bc., bd), one subtraction (ac-bd) =x, one addition (ad+bc)= y, and one overall addition x+jy. 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. This paper highlights the research on (-1+j)-based binary number system, called Complex Binary Number System (CBNS), as it was presented in a tutorial at the IEEE SoutheastCon 2018.

AB - Complex numbers play an important role in engineering applications such as digital signal processing and image processing. To represent these numbers in binary, a 'divide-and-conquer'' technique is used in today's computer systems wherein 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, (a+jb) and (c+ jd), requires two separate additions, (a+c) and (b+d), while multiplication of the same two complex numbers requires four individual multiplications (ac., ad., bc., bd), one subtraction (ac-bd) =x, one addition (ad+bc)= y, and one overall addition x+jy. 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. This paper highlights the research on (-1+j)-based binary number system, called Complex Binary Number System (CBNS), as it was presented in a tutorial at the IEEE SoutheastCon 2018.

KW - associative dataflow

KW - associative memory

KW - Binary number

KW - complex binary number

KW - complex number

KW - computer arithmetic

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U2 - 10.1109/SECON.2018.8478931

DO - 10.1109/SECON.2018.8478931

M3 - Conference contribution

VL - 2018-April

BT - Southeastcon 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -