用3-8译码器设计实现三变量逻辑表达式.

素颜马尾好姑娘i 2023-06-03 03:55 17阅读 0赞

题: 用3-8译码器设计实现逻辑表达式![Y=AB+\\overline\{C\}][Y_AB_overline_C], 可以选择合适的逻辑门配合实现.

(1)写出最小项表达式.

![Y=AB+\\overline\{C\}=AB(C+\\overline\{C\})+(AB+\\overline\{A\}B+A\\overline\{B\}+\\overline\{A\}\\cdot\\overline\{B\})\\overline\{C\}=ABC+AB\\overline\{C\}+\\overline\{A\}B\\overline\{C\}+A\\overline\{B\}\\cdot\\overline\{C\}+\\overline\{A\}\\cdot\\overline\{B\}\\cdot\\overline\{C\}=\\Sigma m(0, 2, 4, 6, 7)=m\_\{7\}+m\_\{6\}+m\_\{4\}+m\_\{2\}+m\_\{0\}.][Y_AB_overline_C_AB_C_overline_C_AB_overline_A_B_A_overline_B_overline_A_cdot_overline_B_overline_C_ABC_AB_overline_C_overline_A_B_overline_C_A_overline_B_cdot_overline_C_overline_A_cdot_overline_B_cdot_overline_C_Sigma m_0_ 2_ 4_ 6_ 7_m_7_m_6_m_4_m_2_m_0_.]

(2)转换表达式为译码输出表达式, 并转换为与非形式.

![Y=m\_\{7\}+m\_\{6\}+m\_\{4\}+m\_\{2\}+m\_\{0\}=\\overline\{Y\_\{7\}\}+\\overline\{Y\_\{6\}\}+\\overline\{Y\_\{4\}\}+\\overline\{Y\_\{2\}\}+\\overline\{Y\_\{0\}\}=\\overline\{Y\_\{0\}Y\_\{2\}Y\_\{4\}Y\_\{6\}Y\_\{7\}\}.][Y_m_7_m_6_m_4_m_2_m_0_overline_Y_7_overline_Y_6_overline_Y_4_overline_Y_2_overline_Y_0_overline_Y_0_Y_2_Y_4_Y_6_Y_7_.]

(3)绘制逻辑图:![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70][]

在图中, ![E\_\{3\}][E_3]连接一个赋值电阻, 赋值为1. ![E\_\{2\}E\_\{1\}][E_2_E_1]接电源负极, 表示赋值为00. 此时![E\_\{3\}E\_\{2\}E\_\{1\}=100][E_3_E_2_E_1_100], 译码器处于译码状态中, 译码信号输入与非门实现了表达式所表示的功能.

[Y_AB_overline_C]: https://private.codecogs.com/gif.latex?Y%3DAB&plus;%5Coverline%7BC%7D
[Y_AB_overline_C_AB_C_overline_C_AB_overline_A_B_A_overline_B_overline_A_cdot_overline_B_overline_C_ABC_AB_overline_C_overline_A_B_overline_C_A_overline_B_cdot_overline_C_overline_A_cdot_overline_B_cdot_overline_C_Sigma m_0_ 2_ 4_ 6_ 7_m_7_m_6_m_4_m_2_m_0_.]: https://private.codecogs.com/gif.latex?Y%3DAB&plus;%5Coverline%7BC%7D%3DAB%28C&plus;%5Coverline%7BC%7D%29&plus;%28AB&plus;%5Coverline%7BA%7DB&plus;A%5Coverline%7BB%7D&plus;%5Coverline%7BA%7D%5Ccdot%5Coverline%7BB%7D%29%5Coverline%7BC%7D%3DABC&plus;AB%5Coverline%7BC%7D&plus;%5Coverline%7BA%7DB%5Coverline%7BC%7D&plus;A%5Coverline%7BB%7D%5Ccdot%5Coverline%7BC%7D&plus;%5Coverline%7BA%7D%5Ccdot%5Coverline%7BB%7D%5Ccdot%5Coverline%7BC%7D%3D%5CSigma%20m%280%2C%202%2C%204%2C%206%2C%207%29%3Dm_%7B7%7D&plus;m_%7B6%7D&plus;m_%7B4%7D&plus;m_%7B2%7D&plus;m_%7B0%7D.
[Y_m_7_m_6_m_4_m_2_m_0_overline_Y_7_overline_Y_6_overline_Y_4_overline_Y_2_overline_Y_0_overline_Y_0_Y_2_Y_4_Y_6_Y_7_.]: https://private.codecogs.com/gif.latex?Y%3Dm_%7B7%7D&plus;m_%7B6%7D&plus;m_%7B4%7D&plus;m_%7B2%7D&plus;m_%7B0%7D%3D%5Coverline%7BY_%7B7%7D%7D&plus;%5Coverline%7BY_%7B6%7D%7D&plus;%5Coverline%7BY_%7B4%7D%7D&plus;%5Coverline%7BY_%7B2%7D%7D&plus;%5Coverline%7BY_%7B0%7D%7D%3D%5Coverline%7BY_%7B0%7DY_%7B2%7DY_%7B4%7DY_%7B6%7DY_%7B7%7D%7D.
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MjA0ODQ2Mw_size_16_color_FFFFFF_t_70]: /images/20230601/af7086dc38184290aa76560f76376c4e.png
[E_3]: https://private.codecogs.com/gif.latex?E_%7B3%7D
[E_2_E_1]: https://private.codecogs.com/gif.latex?E_%7B2%7DE_%7B1%7D
[E_3_E_2_E_1_100]: https://private.codecogs.com/gif.latex?E_%7B3%7DE_%7B2%7DE_%7B1%7D%3D100