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# System prepended metadata

title: Digital Circuit Design HW#5
tags: [homework]

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---
tags: homework
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# Digital Circuit Design HW#5

## 5.2
![](https://i.imgur.com/8lmn5kb.png)

2-1 MUX: 
$Output=S'I_0+SI_1$

JK flip-flop:
$D=JQ'+K'Q$

![](https://i.imgur.com/DDciS0z.png)


## 5.6
![](https://i.imgur.com/aKx2jg2.png)

### a. 
![](https://i.imgur.com/1fcoJiT.png)

### b.
| Present(A/B) | Input(x/y) | Next(A/B) | Output(z) |
|:------------:|:----------:|:---------:|:---------:|
|     0/0      |    0/0     |    0/0    |     0     |
|     0/0      |    0/1     |    0/0    |     0     |
|     0/0      |    1/0     |    1/1    |     0     |
|     0/0      |    1/1     |    0/1    |     0     |
|     0/1      |    0/0     |    0/0    |     0     |
|     0/1      |    0/1     |    0/0    |     0     |
|     0/1      |    1/0     |    1/0    |     0     |
|     0/1      |    1/1     |    1/0    |     0     |
|     1/0      |    0/0     |    0/0    |     1     |
|     1/0      |    0/1     |    0/0    |     1     |
|     1/0      |    1/0     |    1/1    |     1     |
|     1/0      |    1/1     |    0/1    |     1     |
|     1/1      |    0/0     |    0/0    |     1     |
|     1/1      |    0/1     |    0/0    |     1     |
|     1/1      |    1/0     |    1/1    |     1     |
|     1/1      |    1/1     |    1/1    |     1     |

### c.
![](https://i.imgur.com/vH9hDlw.png)



## 5.16 b
![](https://i.imgur.com/4kPQuXd.png)

$A=x'A+xB$
$B=x'B+xB'$

![](https://i.imgur.com/XVCj2Ge.png)


## 5.19
![](https://i.imgur.com/PCLxEYm.png)

![](https://i.imgur.com/IF82cSv.png)

$y=xA'$
$A=xA'B'$
$B=A+xB+x'C'$
$C=xA+x'C+x'A'B'$

### a
不小心多畫了 D type flip flop 就順便放上來
![](https://i.imgur.com/0YpuTnW.png)

### b
![](https://i.imgur.com/hOlAoxp.png =600x)