### Abstract

This study proposes an algorithm for generating the associated Boolean expression in VHDL, given a ladder diagram (LD) as the input. The purpose of the algorithm is to implement of field-programmable gate array-(FPGA-) based programmable logic controllers (PLCs), where an effective conversion from an LD to its associated Boolean expressions seems rarely mentioned. Based on this core thought, the conversion process of the algorithm first involves abstracting and expressing the encountered LD as an activity-on-vertex (AOV) graph. Next, an AND-OR tree in which AND-nodes and OR-nodes connote the series and the parallel relationships between the vertices of the AOV graph is constructed based on the AOV graph. Therefore, by a traversal to the AND-OR tree, the associated Boolean expression, as the output of the algorithm, can be easily obtained in VHDL. The proposed algorithm is then verified with an illustrative example, wherein a complicated LD is given as the input.

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

Article number | 530586 |

Journal | Mathematical Problems in Engineering |

Volume | 2015 |

DOIs | |

Publication status | Published - 2015 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Problems in Engineering*,

*2015*, [530586]. https://doi.org/10.1155/2015/530586

**An algorithm for generating boolean expressions in VHDL based on ladder diagrams.** / Xie, Hongxia; Zhuang, Zheng Yun.

Research output: Contribution to journal › Article

*Mathematical Problems in Engineering*, vol. 2015, 530586. https://doi.org/10.1155/2015/530586

}

TY - JOUR

T1 - An algorithm for generating boolean expressions in VHDL based on ladder diagrams

AU - Xie, Hongxia

AU - Zhuang, Zheng Yun

PY - 2015

Y1 - 2015

N2 - This study proposes an algorithm for generating the associated Boolean expression in VHDL, given a ladder diagram (LD) as the input. The purpose of the algorithm is to implement of field-programmable gate array-(FPGA-) based programmable logic controllers (PLCs), where an effective conversion from an LD to its associated Boolean expressions seems rarely mentioned. Based on this core thought, the conversion process of the algorithm first involves abstracting and expressing the encountered LD as an activity-on-vertex (AOV) graph. Next, an AND-OR tree in which AND-nodes and OR-nodes connote the series and the parallel relationships between the vertices of the AOV graph is constructed based on the AOV graph. Therefore, by a traversal to the AND-OR tree, the associated Boolean expression, as the output of the algorithm, can be easily obtained in VHDL. The proposed algorithm is then verified with an illustrative example, wherein a complicated LD is given as the input.

AB - This study proposes an algorithm for generating the associated Boolean expression in VHDL, given a ladder diagram (LD) as the input. The purpose of the algorithm is to implement of field-programmable gate array-(FPGA-) based programmable logic controllers (PLCs), where an effective conversion from an LD to its associated Boolean expressions seems rarely mentioned. Based on this core thought, the conversion process of the algorithm first involves abstracting and expressing the encountered LD as an activity-on-vertex (AOV) graph. Next, an AND-OR tree in which AND-nodes and OR-nodes connote the series and the parallel relationships between the vertices of the AOV graph is constructed based on the AOV graph. Therefore, by a traversal to the AND-OR tree, the associated Boolean expression, as the output of the algorithm, can be easily obtained in VHDL. The proposed algorithm is then verified with an illustrative example, wherein a complicated LD is given as the input.

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U2 - 10.1155/2015/530586

DO - 10.1155/2015/530586

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AN - SCOPUS:84924246225

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JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

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