Fundamentals of digital circuit (IV) data distributor, data selector and numerical comparator

Fundamentals of digital circuits （ Four ） Data distributor 、 Data selector and numeric comparator

One 、 Data distributor

In the process of data transmission , The data selector can allocate the data of a certain way to different data channels , This circuit is called a data distributor . abbreviation DEMUX, Generally, there are already input and multiple outputs . The following figure shows the chip integration diagram of a four-way data selector ：

It can be D Send to the channel selected by the data variable , The following figure is the truth table of the data selector ：

You can see ,$A$ and $B$ The two digits represent the binary code of the output circuit , It is called selection input . The function expression of each path is ：
$W_0=D\overline{AB}$
$W_1=D\overline{A}B$
$W_2=DA\overline{B}$
$W_0=DAB$

Two 、 Data selector

Data selector abbreviation MUX. Its logic function is under the control of address selection signal , Select one output from multiple data .
74153 It is a data selector of one out of four , The following figure shows its chip pin distribution ：

among $A_0$,$A_1$ Is the address selector ,$\overline{E}$ Is the enable end , Only if it is entered as 0 when , Data selector can work , Otherwise, the two outputs will output 0.

74151 It is a one out of eight data selector , The following figure shows its chip pin distribution ：

$E$ The end is the enabling end , Only if it is 0 when , Data selector will work , Otherwise, the output end outputs 0; Because it is an eight bit selector , So we need $A_0$$A_1$$A_2$ Three bit selector （$2^3=8$） The picture below is 74151 My menu ：

The output logic function of the data selector is in the form of and or of the sum of the minimum terms , So we can use data selector to realize any logic function .

3、 ... and 、 Numerical comparator

The function of numerical comparator is to compare the size of two binary numbers .
How does the numerical comparator realize comparison ？ Suppose there are two four bit binary numbers $A=A_3{A}_2{A}_1{A}_0$ and $B=B_3{B}_2{B}_1{B}_0$, To compare the size of these two numbers, start from the highest order , If the highest order is not equal , Then it can be said that the number with the largest highest position is larger , The number with the smaller highest position is smaller ; If the highest order is equal , Compare the next , Again , If this bit is not equal , It means that the larger one is , This means that the smaller number is smaller , If this one is also equal , Then continue to compare the next , Until we can distinguish the size of these two numbers .

1. One digit value comparator

First, the truth table of a one digit numerical comparator is given ：

You can write an expression according to the truth table ：
$(A_i=B_i)=\overline{A_i\oplus B_i}$
$(A_i<B_i)=\overline{A_i}{B}_i$
$(A_i>B_i)=A_i\overline{B_i}$
Connect the logic diagram according to the expression .

2. Four digit value comparator

The following figure is the truth table of the four digit numeric comparator ：

No 2-3 Line description as long as the highest order is not equal , Then you can judge the size
In the table 4-9 Row is the case when the highest bits are equal , At this time, it is relatively low , Finally, you can also compare the size
The last three rows in the table are the cases where each of the two numbers is equal , The result at this time is determined by the state of the cascade input , Which cascade input is 1, Then the output of the corresponding output end is 1.

first draft 2022/5/7