### Abstract

Complex numbers play a very important role in various applications of electrical and computer engineering. These days, arithmetic operations dealing with these numbers rely on a "divide-and-conquer" technique wherein a complex number is broken into its real and imaginary parts and then, after representing each part in binary number system, operation is carried out on each part as if part of the real arithmetic. Thus, addition of two complex numbers requires two separate additions and their multiplication requires four individual multiplications, one subtraction and one addition. In an effort to reduce the number of arithmetic operations within the realm of complex arithmetic, binary number system with base (-1+j), called complex binary number system, has been proposed in the literature which allows a complex number to be represented as single-unit instead of two separate units as in the base-2 binary number system. In this paper, the effects of shift-left operations on complex binary numbers have been examined.

Original language | English |
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Title of host publication | Canadian Conference on Electrical and Computer Engineering |

Pages | 2005-2008 |

Number of pages | 4 |

Volume | 2005 |

DOIs | |

Publication status | Published - 2005 |

Event | Canadian Conference on Electrical and Computer Engineering 2005 - Saskatoon, SK, Canada Duration: May 1 2005 → May 4 2005 |

### Other

Other | Canadian Conference on Electrical and Computer Engineering 2005 |
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Country | Canada |

City | Saskatoon, SK |

Period | 5/1/05 → 5/4/05 |

### Fingerprint

### Keywords

- Binary number
- Complex binary number
- Complex number
- Shift-left

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture

### Cite this

*Canadian Conference on Electrical and Computer Engineering*(Vol. 2005, pp. 2005-2008). [1557378] https://doi.org/10.1109/CCECE.2005.1557378

**Effects of shift-left operations on complex binary numbers.** / Jamil, Tariq; Ali, Usman.

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

*Canadian Conference on Electrical and Computer Engineering.*vol. 2005, 1557378, pp. 2005-2008, Canadian Conference on Electrical and Computer Engineering 2005, Saskatoon, SK, Canada, 5/1/05. https://doi.org/10.1109/CCECE.2005.1557378

}

TY - GEN

T1 - Effects of shift-left operations on complex binary numbers

AU - Jamil, Tariq

AU - Ali, Usman

PY - 2005

Y1 - 2005

N2 - Complex numbers play a very important role in various applications of electrical and computer engineering. These days, arithmetic operations dealing with these numbers rely on a "divide-and-conquer" technique wherein a complex number is broken into its real and imaginary parts and then, after representing each part in binary number system, operation is carried out on each part as if part of the real arithmetic. Thus, addition of two complex numbers requires two separate additions and their multiplication requires four individual multiplications, one subtraction and one addition. In an effort to reduce the number of arithmetic operations within the realm of complex arithmetic, binary number system with base (-1+j), called complex binary number system, has been proposed in the literature which allows a complex number to be represented as single-unit instead of two separate units as in the base-2 binary number system. In this paper, the effects of shift-left operations on complex binary numbers have been examined.

AB - Complex numbers play a very important role in various applications of electrical and computer engineering. These days, arithmetic operations dealing with these numbers rely on a "divide-and-conquer" technique wherein a complex number is broken into its real and imaginary parts and then, after representing each part in binary number system, operation is carried out on each part as if part of the real arithmetic. Thus, addition of two complex numbers requires two separate additions and their multiplication requires four individual multiplications, one subtraction and one addition. In an effort to reduce the number of arithmetic operations within the realm of complex arithmetic, binary number system with base (-1+j), called complex binary number system, has been proposed in the literature which allows a complex number to be represented as single-unit instead of two separate units as in the base-2 binary number system. In this paper, the effects of shift-left operations on complex binary numbers have been examined.

KW - Binary number

KW - Complex binary number

KW - Complex number

KW - Shift-left

UR - http://www.scopus.com/inward/record.url?scp=33751340093&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751340093&partnerID=8YFLogxK

U2 - 10.1109/CCECE.2005.1557378

DO - 10.1109/CCECE.2005.1557378

M3 - Conference contribution

VL - 2005

SP - 2005

EP - 2008

BT - Canadian Conference on Electrical and Computer Engineering

ER -