Website: https://vikasdhiman.info/ECE275-Sequential-Logic/

\[
\newcommand{\bx}{\bar{x}}
\newcommand{\by}{\bar{y}}
\newcommand{\bz}{\bar{z}}
\newcommand{\bA}{\bar{A}}
\newcommand{\bB}{\bar{B}}
\newcommand{\bC}{\bar{C}}
\newcommand{\bD}{\bar{D}}
\newcommand{\bE}{\bar{E}}
\]

- Homework 4 has only four problems and is due on Oct 1st Friday by midnight.
- We will review material covered so far on Oct 4th, please email me topics that you want to be reviewed.
- Midterm is on Oct 6th, 9 AM in class. All problems will be variations of the homework problems.

AND gate

\( f(x_1, x_2) = x_1 \cdot x_2 \)

\( f(x_1, x_2) = x_1 \cdot x_2 \)

OR gate

\( f_{\text{OR}}(x_1, x_2) = x_1 + x_2 \)

\( f_{\text{OR}}(x_1, x_2) = x_1 + x_2 \)

NOT gate

\( L_{\text{NOT}}(x_1) = \bar{x}_1 \)

\( L_{\text{NOT}}(x_1) = \bar{x}_1 \)

NAND gate

\( Q = \overline{x_1 \cdot x_2} \)

\( Q = \overline{x_1 \cdot x_2} \)

NOR gate

\( Q = \overline{x_1 + x_2} \)

\( Q = \overline{x_1 + x_2} \)

XOR gate

\( Q = \bx_1 x_2 + x_1 \bx_2 = x_1 \oplus x_2 \)

\( Q = \bx_1 x_2 + x_1 \bx_2 = x_1 \oplus x_2 \)

- Factorization
- Functional decomposition

\(\bar{x}_1\) | \(x_1 \) | ||||
---|---|---|---|---|---|

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 0 | 0 | 0 | 0 |

\(x_4\) | 1 | 0 | 1 | 0 | |

\(x_3\) | 1 | 1 | 1 | 1 | |

\(\bar{x}_4\) | 0 | 1 | 0 | 1 |

\(\bar{x}_1\) | \(x_1 \) | ||||
---|---|---|---|---|---|

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 1 | 0 | 0 | 1 |

\(x_4\) | 0 | 0 | 0 | 0 | |

\(x_3\) | 0 | 0 | 0 | 0 | |

\(\bar{x}_4\) | 0 | 1 | 1 | 0 |

\(\bx_5 \) | |||||
---|---|---|---|---|---|

\(\bar{x}_1\) | \(x_1 \) | ||||

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 1 | 0 | 0 | 0 |

\(x_4\) | 0 | 1 | 1 | 1 | |

\(x_3\) | 1 | 0 | 0 | 0 | |

\(\bar{x}_4\) | 0 | 1 | 1 | 1 |

\(x_5 \) | |||||
---|---|---|---|---|---|

\(\bar{x}_1\) | \(x_1 \) | ||||

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 0 | 0 | 0 | 0 |

\(x_4\) | 1 | 1 | 1 | 1 | |

\(x_3\) | 0 | 0 | 0 | 0 | |

\(\bar{x}_4\) | 1 | 1 | 1 | 1 |

\(\bx_5 \) | |||||
---|---|---|---|---|---|

\(\bar{x}_1\) | \(x_1 \) | ||||

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 1 | 0 | 0 | 0 |

\(x_4\) | 0 | 1 | 1 | 1 | |

\(x_3\) | 1 | 0 | 0 | 0 | |

\(\bar{x}_4\) | 0 | 1 | 1 | 1 |

\(x_5 \) | |||||
---|---|---|---|---|---|

\(\bar{x}_1\) | \(x_1 \) | ||||

\(\bar{x}_2\) | \(x_2 \) | \(\bar{x}_2\) | |||

\(\bar{x}_3\) | \(\bar{x}_4\) | 0 | 0 | 0 | 0 |

\(x_4\) | 1 | 1 | 1 | 1 | |

\(x_3\) | 0 | 0 | 0 | 0 | |

\(\bar{x}_4\) | 1 | 1 | 1 | 1 |

\(\bA \) | |||||
---|---|---|---|---|---|

\(\bB\) | \(B \) | ||||

\(\bC\) | \(C \) | \(\bC\) | |||

\(\bD\) | \(\bE\) | 0 | 1 | 1 | 1 |

\(E\) | 1 | 0 | 0 | 0 | |

\(D\) | 0 | 1 | 1 | 1 | |

\(\bE\) | 1 | 0 | 0 | 0 |

\(\bA \) | |||||
---|---|---|---|---|---|

\(\bB\) | \(B \) | ||||

\(\bC\) | \(C \) | \(\bC\) | |||

\(\bD\) | \(\bE\) | 1 | 0 | 0 | 0 |

\(E\) | 0 | 1 | 0 | 0 | |

\(D\) | 1 | 0 | 0 | 0 | |

\(\bE\) | 0 | 1 | 0 | 0 |