Digital-electronics 简明教程

Digital Electronics - Conversion of Flip-Flops

在上一章中，我们讨论了四个触发器，即 SR 触发器、D 触发器、JK 触发器和 T 触发器。我们可以通过添加一些额外的逻辑将一个触发器转换为另外三个触发器。因此，总共将有十二个 flip-flop conversions 。

In previous chapter, we discussed the four flip-flops, namely SR flip-flop, D flip-flop, JK flip-flop & T flip-flop. We can convert one flip-flop into the remaining three flip-flops by including some additional logic. So, there will be total of twelve flip-flop conversions.

遵循这些 steps 以将一个触发器转换为另一个触发器。

Follow these steps for converting one flip-flop to the other.

Consider the characteristic table of desired flip-flop.
Fill the excitation values (inputs) of given flip-flop for each combination of present state and next state. The excitation table for all flip-flops is shown below.

Present State	Next State	SR Flip-Flop Inputs	D flip-flop input	JK Flip-Flop Inputs	T Flip-Flop Input
Q(t)	Q(t+1)	S	R	D	J
K	T	0	0	0	x
0	0	x	0	0	1
1	0	1	1	x	1
1	0	0	1	0	x
1	1	1	1	x	0

获得每个激励输入的 simplified expressions 。如有必要，使用 K 图进行简化。

Get the simplified expressions for each excitation input. If necessary, use Kmaps for simplifying.

根据使用给定触发器和必要的逻辑门简化的表达式绘制 circuit diagram 的所需触发器。

Draw the circuit diagram of desired flip-flop according to the simplified expressions using given flip-flop and necessary logic gates.

现在，让我们将几个触发器转换为其他触发器。对其余触发器转换遵循相同的过程。

Now, let us convert few flip-flops into other. Follow the same process for remaining flipflop conversions.

SR Flip-Flop to other Flip-Flop Conversions

以下是 SR 触发器到其他触发器的三种可能性转换。

Following are the three possible conversions of SR flip-flop to other flip-flops.

SR Flip-Flop to D Flip-Flop
SR Flip-Flop to JK Flip-Flop
SR Flip-Flop to T Flip-Flop

SR Flip-Flop to D Flip-Flop Conversion

此处，给定的触发器是 SR 触发器，所需触发器是 D 触发器。因此，考虑 D 触发器的以下 characteristic table 。

Here, the given flip-flop is SR flip-flop and the desired flip-flop is D flip-flop. Therefore, consider the following characteristic table of D flip-flop.

D Flip-Flop Input	Present State	Next State
D	Q(t)	Q(t + 1)
0	0	0
0	1	0
1	0	1
1	1	1

我们知道 SR 触发器有两个输入 S 和 R。因此，写下 SR 触发器每个当前状态和下一个状态值组合的激励值。下表显示了 D 触发器的特性表以及 SR 触发器的 excitation inputs 。

We know that SR flip-flop has two inputs S & R. So, write down the excitation values of SR flip-flop for each combination of present state and next state values. The following table shows the characteristic table of D flip-flop along with the excitation inputs of SR flip-flop.

D Flip-Flop Input	Present State	Next State	SR Flip-Flop Inputs
D	Q(t)	Q(t + 1)	S
R	0	0	0
0	x	0	1
0	0	1	1
0	1	1	0
1	1	1	x

从上表中，我们可以为每个输入写出 Boolean functions ，如下所示。

From the above table, we can write the Boolean functions for each input as below.

\mathrm{S \: = \: m_{2} \: + \: d_{3}}

\mathrm{R \: = \: m_{1} \: + \: d_{0}}

我们可以使用 2 个变量 K 映射来获得这些输入的简化表达式。S 和 R 的 k-Maps 如下所示。

We can use 2 variable K-Maps for getting simplified expressions for these inputs. The k-Maps for S & R are shown below.

因此，在简化后，我们得到 S = D 和 R = D'。D 触发器的 circuit diagram 如下图所示。

So, we got S = D & R = D' after simplifying. The circuit diagram of D flip-flop is shown in the following figure.

此电路由 SR 触发器和反相器组成。此反相器生成一个输出，它是输入 D 的补码。因此，整体电路具有单个输入 D 和两个输出 Q(t) 和 Q(t)'。因此，它是一个 D flip-flop 。同样，你还可以进行其他两种转换。

This circuit consists of SR flip-flop and an inverter. This inverter produces an output, which is complement of input, D. So, the overall circuit has single input, D and two outputs Q(t) & Q(t)'. Hence, it is a D flip-flop. Similarly, you can do other two conversions.

D Flip-Flop to other Flip-Flop Conversions

以下是 D 触发器到其他触发器的三种可能转换。

Following are the three possible conversions of D flip-flop to other flip-flops.

D Flip-Flop to T Flip-Flop
D Flip-Flop to SR Flip-Flop
D Flip-Flop to JK Flip-Flop

D Flip-Flop to T Flip-Flop conversion

此处，给定的触发器是 D 触发器，而所需的触发器是 T 触发器。因此，考虑 T 触发器的以下 characteristic table 。

Here, the given flip-flop is D flip-flop and the desired flip-flop is T flip-flop. Therefore, consider the following characteristic table of T flip-flop.

T Flip-Flop Input	Present State	Next State
T	Q(t)	Q(t + 1)
0	0	0
0	1	1
1	0	1
1	1	0

我们知道 D 触发器具有单个输入 D。因此，写下 D 触发器在当前状态和下一个状态值的每个组合下的激励值。下表显示了 T 触发器的特性表以及 excitation input D 触发器的特性表。

We know that D flip-flop has single input D. So, write down the excitation values of D flip-flop for each combination of present state and next state values. The following table shows the characteristic table of T flip-flop along with the excitation input of D flip-flop.

T Flip-Flop Input	Present State	Next State	D Flip-Flop Input
T	Q(t)	Q(t + 1)	D
0	0	0	0
0	1	1	1
1	0	1	1
1	1	0	0

从上表中，我们可以直接写出 D Boolean function 的值，如下所示。

From the above table, we can directly write the Boolean function of D as below.

\mathrm{D \: = \: T \: \oplus \: Q \: \left ( t \: \right )}

因此，我们要求一个两个输入的异或门和 D 触发器。 circuit diagram T 触发器的值如下图所示。

So, we require a two input Exclusive-OR gate along with D flip-flop. The circuit diagram of T flip-flop is shown in the following figure.

该电路由 D 触发器和异或门组成。此异或门生成一个输出，它是 T 和 Q(t) 的异或值。因此，整体电路具有单个输入 T 和两个输出 Q(t) 和 Q(t)'。因此，它是一个 T flip-flop 。同样，你还可以进行其他两种转换。

This circuit consists of D flip-flop and an Exclusive-OR gate. This Exclusive-OR gate produces an output, which is Ex-OR of T and Q(t). So, the overall circuit has single input, T and two outputs Q(t) & Q(t)’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

JK Flip-Flop to other Flip-Flop Conversions

以下是 JK 触发器到其他触发器的三种可能转换。

Following are the three possible conversions of JK flip-flop to other flip-flops.

JK Flip-Flop to T Flip-Flop
JK Flip-Flop to D Flip-Flop
JK Flip-Flop to SR Flip-Flop

JK Flip-Flop to T Flip-Flop conversion

此处，给定的触发器是 JK 触发器，而所需的触发器是 T 触发器。因此，考虑 T 触发器的以下 characteristic table 。

Here, the given flip-flop is JK flip-flop and the desired flip-flop is T flip-flop. Therefore, consider the following characteristic table of T flip-flop.

T Flip-Flop Input	Present State	Next State
T	Q(t)	Q(t + 1)
0	0	0
0	1	1
1	0	1
1	1	0

我们知道 JK 触发器有两个输入 J 和 K。因此，写下 JK 触发器在当前状态和下一个状态值的每个组合下的激励值。下表显示了 T 触发器的特性表以及 excitation inputs JK 触发器的特性表。

We know that JK flip-flop has two inputs J & K. So, write down the excitation values of JK flip-flop for each combination of present state and next state values. The following table shows the characteristic table of T flip-flop along with the excitation inputs of JK flipflop.

T Flip-Flop Input	Present State	Next State	JK Flip-Flop Inputs
T	Q(t)	Q(t + 1)	J
K	0	0	0
0	x	0	1
1	x	0	1
0	1	1	x
1	1	0	x

从上表中，我们可以为每个输入写出 Boolean functions ，如下所示。

From the above table, we can write the Boolean functions for each input as below.

\mathrm{J \: = \: m_{2} \: + \: d_{1} \: + \: d_{3}}

\mathrm{K \: = \: m_{3} \: + \: d_{0} \: + \: d_{2}}

我们可以使用 2 个变量 K 图获取这些两个输入的简化表达式。J 和 K 的 k-Maps 如下所示。

We can use 2 variable K-Maps for getting simplified expressions for these two inputs. The k-Maps for J & K are shown below.

于是，我们获得了 J = T 和 K = T（简化后）。T 触发器的 circuit diagram 如下图所示。

So, we got, J = T & K = T after simplifying. The circuit diagram of T flip-flop is shown in the following figure.

circuit diagram of t flip flop with jk flipflop

此电路仅由 JK 触发器组成。无需任何其他门。只需将同一输入 T 连接到 J 和 K。因此，整个电路有一个输入 T 和两个输出 Q(t) 和 Q(t)'。因此，它是一个 T flip-flop 。类似地，可以执行其他两个转换。

This circuit consists of JK flip-flop only. It doesn’t require any other gates. Just connect the same input T to both J & K. So, the overall circuit has single input, T and two outputs Q(t) & Q(t)’. Hence, it is a T flip-flop. Similarly, you can do other two conversions.

T Flip-Flop to other Flip-Flop Conversions

以下是 T 触发器到其他触发器的三种可能转换。

Following are the three possible conversions of T flip-flop to other flip-flops.

T Flip-Flop to D Flip-Flop
T Flip-Flop to SR Flip-Flop
T Flip-Flop to JK Flip-Flop

T Flip-Flop to D Flip-Flop conversion

在此，给定触发器是 T 触发器，所需触发器是 D 触发器。因此，考虑 D 触发器的特性表，并为当前状态和下一状态值中的每种组合写下 T 触发器的激发值。下表显示了 D 触发器的 characteristic table 以及 T 触发器的 excitation input 。

Here, the given flip-flop is T flip-flop and the desired flip-flop is D flip-flop. Therefore, consider the characteristic table of D flip-flop and write down the excitation values of T flip-flop for each combination of present state and next state values. The following table shows the characteristic table of D flip-flop along with the excitation input of T flip-flop.

D Flip-Flop Input	Present State	Next State	T Flip-Flop Input
D	Q(t)	Q(t + 1)	T
0	0	0	0
0	1	0	1
1	0	1	1
1	1	1	0

从上表中，我们可以直接写出 T 的布尔函数，如下所示。

From the above table, we can directly write the Boolean function of T as below.

\mathrm{T \: = \: D \: \oplus \: Q \left ( t \right )}

因此，我们需要一个双输入异或门以及 T 触发器。D 触发器的 circuit diagram 如下图所示。

So, we require a two input Exclusive-OR gate along with T flip-flop. The circuit diagram of D flip-flop is shown in the following figure.

此电路由 T 触发器和异或门组成。此异或门产生一个输出，即 D 和 Q(t) 的异或。因此，整个电路有一个输入 D 和两个输出 Q(t) 和 Q(t)'。因此，它是一个 D flip-flop 。类似地，可以执行其他两个转换。

This circuit consists of T flip-flop and an Exclusive-OR gate. This Exclusive-OR gate produces an output, which is Ex-OR of D and Q(t). So, the overall circuit has single input, D and two outputs Q(t) & Q(t)’. Hence, it is a D flip-flop. Similarly, you can do other two conversions.