同步四进制可逆加减法计数器分析

川长思鸟来 2023-06-03 09:55 13阅读 0赞

(10分)分析下图电路, 写出驱动方程、状态方程, 并画出状态转换图, 之后判断该电路实现的逻辑功能.

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70][]

分析同步时序逻辑电路时要遵循的思维过程:

①确定触发器类型(JK触发器/D触发器/......) -> ②写出触发器状态特性方程 -> ③根据逻辑图写出输出方程, 并作可能的化简, -> ④根据逻辑图写出激励方程组, 并作可能的化简, -> ⑤将求出的激励方程组代入触发器状态特性方程, 求出次态方程组, -> ⑥根据求出的次态方程组列状态表, -> ⑦根据绘制好的状态表绘制状态图, -> ⑧仔细观察状态图, 寻找状态转换规律, 最终分析出电路的逻辑功能.

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70 1][]

对于Y的推理, 不建议像图片中这样做(我的推理走了弯路) : 应从![Y=\\overline\{ \\overline\{\\overline\{A\}\{Q\_\{1\}\}^\{n\}\{Q\_\{2\}\}^\{n\}\} \\cdot \\overline\{A \\cdot \\overline\{\{Q\_\{1\}\}^\{n\}\} \\cdot \\overline\{\{Q\_\{2\}\}^\{n\}\}\} \}][Y_overline_ _overline_overline_A_Q_1_n_Q_2_n_ _cdot _overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_]入手.

Y=1时, ![\\overline\{\\overline\{A\}\{Q\_\{1\}\}^\{n\}\{Q\_\{2\}\}^\{n\}\} \\cdot \\overline\{A \\cdot \\overline\{\{Q\_\{1\}\}^\{n\}\} \\cdot \\overline\{\{Q\_\{2\}\}^\{n\}\}\}=0][overline_overline_A_Q_1_n_Q_2_n_ _cdot _overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_0], 那么![\\overline\{\\overline\{A\}\{Q\_\{1\}\}^\{n\}\{Q\_\{2\}\}^\{n\}\}=0][overline_overline_A_Q_1_n_Q_2_n_0]或![\\overline\{A \\cdot \\overline\{\{Q\_\{1\}\}^\{n\}\} \\cdot \\overline\{\{Q\_\{2\}\}^\{n\}\}\}\}=0][overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_0], 则![\\overline\{A\}\{Q\_\{1\}\}^\{n\}\{Q\_\{2\}\}^\{n\}=1][overline_A_Q_1_n_Q_2_n_1]或![A \\cdot \\overline\{\{Q\_\{1\}\}^\{n\}\} \\cdot \\overline\{\{Q\_\{2\}\}^\{n\}\}\}=1][A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_1].

有了该结论, 我们可以轻松地填充图示卡诺图, 并得出Y的最简与或表达式.

[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70]: /images/20230601/08ed8b8ae1094f4a88a629c7ba15e676.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70 1]: /images/20230601/a4933385484f4f2e9fe2da98b51de950.png
[Y_overline_ _overline_overline_A_Q_1_n_Q_2_n_ _cdot _overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_]: https://private.codecogs.com/gif.latex?Y%3D%5Coverline%7B%20%5Coverline%7B%5Coverline%7BA%7D%7BQ_%7B1%7D%7D%5E%7Bn%7D%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7BA%20%5Ccdot%20%5Coverline%7B%7BQ_%7B1%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7B%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%7D%20%7D
[overline_overline_A_Q_1_n_Q_2_n_ _cdot _overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_0]: https://private.codecogs.com/gif.latex?%5Coverline%7B%5Coverline%7BA%7D%7BQ_%7B1%7D%7D%5E%7Bn%7D%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7BA%20%5Ccdot%20%5Coverline%7B%7BQ_%7B1%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7B%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%7D%3D0
[overline_overline_A_Q_1_n_Q_2_n_0]: https://private.codecogs.com/gif.latex?%5Coverline%7B%5Coverline%7BA%7D%7BQ_%7B1%7D%7D%5E%7Bn%7D%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%3D0
[overline_A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_0]: https://private.codecogs.com/gif.latex?%5Coverline%7BA%20%5Ccdot%20%5Coverline%7B%7BQ_%7B1%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7B%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%7D%7D%3D0
[overline_A_Q_1_n_Q_2_n_1]: https://private.codecogs.com/gif.latex?%5Coverline%7BA%7D%7BQ_%7B1%7D%7D%5E%7Bn%7D%7BQ_%7B2%7D%7D%5E%7Bn%7D%3D1
[A _cdot _overline_Q_1_n_ _cdot _overline_Q_2_n_1]: https://private.codecogs.com/gif.latex?A%20%5Ccdot%20%5Coverline%7B%7BQ_%7B1%7D%7D%5E%7Bn%7D%7D%20%5Ccdot%20%5Coverline%7B%7BQ_%7B2%7D%7D%5E%7Bn%7D%7D%7D%3D1