Level 1: 2-to-1 selector design
If you have any doubts or want the final experimental code, you can shout in the comment area. I hope my answer will be helpful to you. Please pay attention and go, thank you! ! !
The final answer for this level:
mission details
- The task of this level: draw a 2-to-1 multiplexer in Logisim, complete the test locally, experience the function of data selection, and then complete the evaluation online.
related information
A multiplexer, also known as a data selector, multiplexer, or multiplexer (MUX, Multiplexer), is a circuit that can select any one of the data to be sent to the output end according to the need in the process of multiplexing data transmission. The schematic diagram of the 2-to-1 multiplexer circuit is as follows:
The simplified truth table of the 2-way selector is as follows:
s |
f |
|---|---|
| 0 | w0 |
| 1 | w1 |
Expression: On the basis of this figure, use the blocking feature of the gate circuit to construct the enable signal, and pay attention to the output value when the enable is invalid.f=sw0+sw1
Pin Description
| Signal | I / O | bit width | illustrate |
|---|---|---|---|
| nEnable | enter | 1 person | Enable terminal, active low. Select when nEnable=0; disable selection when nEnable=1, the output is always 1 at this time. |
| Select | enter | 1 person | Address Selection (Data Port Selection) |
| D1, D0 | enter | 1 person | 2 data input |
| F | output | 1 person | data output |
Subcircuit appearance
Do not move the pin position or the test will not be completed!
Experimental content
Experimental circuit framework MUXlab.circ download: Right-click the code area on the right, Download File
Open the experimental circuit framework in Logisim, and complete the selector design in the "2-to-1 MUX" subcircuit in the project.
test introduction
After the local experiment is completed, please open the circuit file (MUXlab.circ) with Notepad or other plain text editor, select all, copy, and paste it into the Educoder code window, click the "Evaluation" button at the bottom right, and the platform will evaluate you. code to test.
Level 2: 4-to-1 selector design
If you have any doubts or want the answer code, you can call me in the comment area, I hope my answer will be helpful to you, click on it and go, thank you! ! !
The final answer for this level:
mission details
The task of this level: Use the 2-to-1 selector of the previous level to cascade design a 4-to-1 multiplexer in Logisim.
related information
A multiplexer, also known as a data selector, multiplexer, or multiplexer (MUX, Multiplexer), is a circuit that can select any one of the data to be sent to the output end according to the need in the process of multiplexing data transmission. The 4-to-1 selector cascade expansion principle is as follows:
The simplified truth table of the 4-way selector is as follows:
s1 |
s0 |
f |
|---|---|---|
| 0 | 0 | w0 |
| 0 | 1 | w1 |
| 1 | 0 | w2 |
| 1 | 1 | w3 |
The expression is as follows: is the minimum term f=s1s0w0+s1s0w1+s1s0w2+s1s0w3 =m0w0+m1w1+m2w2+m3w3=∑i=03miwi miof the selection variable , is the data inputs1,s0wi
Pin Description
| Signal | I / O | bit width | illustrate |
|---|---|---|---|
| nEnable | enter | 1 person | Enable terminal: select when nEnable=0; disable selection when nEnable=1, the output is always 1 at this time. |
| Select | enter | 2 bits | Address selection |
| D3~D0 | enter | 1 person | 4 data inputs |
| F | output | 1 person | data output |
Subcircuit appearance
Do not move the pin position or the test will not be completed!
Experimental content
The experimental circuit framework is the same as the first level, open the experimental circuit framework in Logisim, and complete the selector design in the "4 choose 1 MUX" subcircuit.
test introduction
After the local experiment is completed, please open the circuit file (MUXlab.circ) with Notepad or other plain text editor, select all, copy, and paste it into the Educoder code window, click the "Evaluation" button at the bottom right, and the platform will evaluate you. code to test.
Level 3: 1 out of 8 selector design
If you have any doubts or want the answer code, you can call me in the comment area, I hope my answer will be helpful to you, click on it and go, thank you! ! !
The final answer for this level:
mission details
The task of this level: Use the selectors of the previous two levels to cascade to design an 8-to-1 multiplexer.
related information
A multiplexer, also known as a data selector, multiplexer, or multiplexer (MUX, Multiplexer), is a circuit that can select any one of the data to be sent to the output end according to the need in the process of multiplexing data transmission. The simplified truth table of the 8-way selector is as follows:
s2 |
s1 |
s0 |
f |
|---|---|---|---|
| 0 | 0 | 0 | w0 |
| 0 | 0 | 1 | w1 |
| 0 | 1 | 0 | w2 |
| 0 | 1 | 1 | w3 |
| 1 | 0 | 0 | w4 |
| 1 | 0 | 1 | w5 |
| 1 | 1 | 0 | w6 |
| 1 | 1 | 1 | w7 |
The expression is as follows: is the minimum term f=∑i=07miwi miof the selection variable , is the data inputs2,s1,s0wi
Pin Description
| Signal | I / O | bit width | illustrate |
|---|---|---|---|
| nEnable | enter | 1 person | Enable terminal: select when nEnable=0; disable selection when nEnable=1, the output is always 1 at this time. |
| Select | enter | 3 digits | Address selection |
| D7~D0 | enter | 1 person | 8 data inputs |
| F | output | 1 person | data output |
Subcircuit appearance
Do not move the pin position or the test will not be completed!
Experimental content
The experimental circuit framework is the same as the first level, open the experimental circuit framework in Logisim, and complete the selector design in the "8-to-1 MUX" subcircuit.
test introduction
After the local experiment is completed, please open the circuit file (MUXlab.circ) with Notepad or other plain text editor, select all, copy, and paste it into the Educoder code window, click the "Evaluation" button at the bottom right, and the platform will evaluate you. code to test.
Level 4: Application of the Multiplexer
If you have any doubts or want the answer code, you can call me in the comment area, I hope my answer will be helpful to you, click on it and go, thank you! ! !
The final answer for this level:
mission details
The task of this level: Select the multiplexer designed in the previous level in Logisim to design the combinational logic and design the full adder FA.
related information
For the way selector, the expression is as follows: is the minimum term of the selection variable , is the data input2nf=∑i=02n−1miwi misn−1…s0wi
truth table transformation
Principle: Transform the truth table of the function to be implemented into a simplified truth table form corresponding to the multiplexer! For example: use 4 to choose 1 MUX to realize the 3-input multi-function functionf(w1,w2,w3)=Σm(3,5,6,7)
Use 4 to choose 1 MUX to achieve as follows:
w1,w2作为选择变量s1,s0，将0、w3、w3和1分别接入0号、1号、2号和3号数据端口。注意函数变量与选择变量的对应顺序！！ 若用8选1MUX实现3输入函数，则真值表无需做任何变换！ 此时，w1,w2,⋯,w8作为选择变量s7,s6,⋯,s0，将8个函数值分别送入对应数据端口。
香农展开（1变量展开）
任何n变量函数f(w1,w2,⋯,wn)可以对w1展开表示为： f=w1⋅f(0,w2,⋯,wn)+w1⋅f(1,w2,⋯,wn) =w1⋅fw1+w1⋅fw1 对任意wi展开都有效！ 此时可以用2选1MUX实现该函数，如图所示：
w1作为选择变量s，将fw1和fw1的逻辑实现分别接入0号和1号数据端口。
香农展开（2变量展开）
任何n变量函数f(w1,w2,w3,⋯,wn)可以对w1,w2展开表示为： f=w1w2⋅f(0,0,w3,⋯,wn)+w1w2⋅f(0,1,w3,⋯,wn) +w1w2⋅f(1,0,w3,⋯,wn)+w1w2⋅f(1,1,w3,⋯,wn) =w1w2⋅fw1w2+w1w2⋅fw1w2+w1w2⋅fw1w2+w1w2⋅fw1w2 对任意wi,wj(i=j)展开都有效！ 此时可以用4选1MUX实现该函数，如图所示：
w1,w2作为选择变量s1,s0，将fw1w2、fw1w2、fw1w2和fw1w2的逻辑实现分别接入0号、1号、2号和3号数据端口。 依此类推，可以对任意的k个变量展开(k≤n)，然后用2k选1MUX实现该函数！当k=n时，展开式为函数的正则SOP式（标准与或式）。
引脚说明
| 信号 | I/O | 位宽 | 说明 |
|---|---|---|---|
| nEnable | 输入 | 1位 | 使能端：nEnable=0时做加法；nEnable=1禁止相加，此时输出恒为1。 |
| A,B,Ci | 输入 | 1位 | 三个相加数 |
| Co,Sum | 输出 | 1位 | 进位输出、和输出 |
子电路外观
请勿移动引脚位置，否则无法完成测试！
Experimental content
The experimental circuit framework is the same as the first level, open the experimental circuit framework in Logisim, and complete the design of the full adder in the "MUX application" subcircuit.
test introduction
After the local experiment is completed, please open the circuit file (MUXlab.circ) with Notepad or other plain text editor, select all, copy, and paste it into the Educoder code window, click the "Evaluation" button at the bottom right, and the platform will evaluate you. code to test.
Extended Design Suggestions
The circuit design and realization of more functions with different variable numbers can be completed locally by using MUX.