Digital-electronics 简明教程
Binary Adder-Subtractor
一个 binary adder-subtractor 是一种用于执行两种基本算术运算（即二进制加法和二进制减法）的数字电路。它是在计算机、计算器等各种数字系统中的一个重要组成部分。
A binary adder-subtractor is a digital circuit that is used to perform two basic arithmetic operations namely, binary addition and binary subtraction. It is an important component in various digital systems like computers, calculators, etc.
使用二进制加减器的最大优势在于，它将加法和减法运算组合在一个电路中，从而带来了更紧凑的尺寸和更低的成本。
The most significant advantage of using a binary adder-subtractor is that it combines the addition and subtraction operations in a single circuit which results in compact size and lower cost.
阅读本章，以了解二进制加减器的电路和操作。
Read this chapter to understand the circuit and operation of a binary adder-subtractor.
What is a Binary Adder-Subtractor?
数字电子学中，有一类数字电路用于执行加法和减法运算，称为二进制加减器。
In digital electronics, there is a digital circuit which employed for performing addition and subtraction operations, it is called a binary adder-subtractor.
二进制加减器是一种专门设计的数字算术电路，它将二进制数字的加法和减法功能结合在单个电路中。
A binary adder-subtractor is a specially designed digital arithmetic circuit that combines the functionality of addition and subtraction of binary numbers in a single circuit.
二进制加减器电路通过按照以下规则对两个二进制数执行二进制加法和减法运算。
A binary adder-subtractor circuit performs the binary addition and subtraction operations on two binary numbers by following the rules given below.
Rules of Binary Addition
执行二进制加法时需要遵循以下规则：
The following rules are to be followed while performing binary addition −
First Bit (A) |
Second Bit (B) |
Sum (A + B) |
Carry |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
Rules of Binary Subtraction
下表显示了执行二进制减法时需要遵循的规则：
The following table shows the rules to be followed while performing binary subtraction −
First Bit (A) |
Second Bit (B) |
Sum (A - B) |
Borrow |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
0 |
以上就是关于二进制加减器的基本介绍以及二进制加法和减法的规则。现在我们来了解二进制加减器的电路结构。
This is all about a basic introduction to binary adder-subtractor and the rules of binary addition and subtraction. Let us now understand the circuit construction of binary adder-subtractor.
Binary Adder-Subtractor Circuit
二进制加减器的逻辑电路由几个全加器电路组成，这些电路串联在一起。它还包括一个由异或门组成的控制电路并执行模式选择功能，即控制电路用于在加法和减法之间切换电路操作。
The logic circuit of a binary adder-subtractor consists of several full-adder circuits connected together. It also consists of a control circuit consisting of XOR gates and performs the mode selection function i.e., the control circuit is used to switch the circuit operation between addition and subtraction.
以下所示的 circuit diagram of a binary adder-subtractor 可以执行两个 4 位二进制数（例如 A 和 B）的加法或减法：
The circuit diagram of a binary adder-subtractor which can perform the addition or subtraction of two 4-bit binary numbers (say A and B) is shown below −
Components of a Binary Adder-Subtractor
二进制加减器的电路由以下主要组件组成：
The circuit of a binary adder-subtractor consists of the following main components −
Full Adders
全加器是一种用于一次执行三个二进制位的加法的二进制算术电路。它产生两个输出，即和和进位。在二进制加减器电路中，全加器电路还可以使用补码机制执行减法运算。
A full adder is a binary arithmetic circuit used to perform the addition of three binary bits at a time. It produces two outputs namely a sum and a carry. In a binary adder-subtractor circuit, the full adder circuit can also perform the subtraction operation using the complement mechanism.
Working of Binary Adder-Subtractor
现在我们来了解上图中所示的二进制加减器电路的操作。
Let us now understand the operation of a binary adder-subtractor circuit shown in the above figure.
上图所示的电路是一个 4 位二进制加减器。因此，它可以执行两个 4 位二进制数（例如 A 和 B）的加法或减法。
The circuit shown in the above figure is a 4-bit binary adder-subtractor. Therefore, it can perform addition or subtraction of two 4-bit binary numbers, say A and B.
在此电路中，输入 M 称为模式输入。它控制电路的操作，如下所述：
In this circuit, the input M is called the mode input. It controls the operation of the circuit as described below −
-
When M = 0, the circuit operates as a binary adder. Under this mode, we get $\mathrm{B_{X} \: \oplus \: 0 \: = \: B_{X}}$. Thus, each full adder receives the inputs Ax and Bx and performs their addition, i.e., Ax + Bx.
-
When M = 1, the circuit operates as a binary subtractor. In this case, we get $\mathrm{B_{X} \: \oplus \: 1 \: = \: B_{X}}$’ and the input carry Cin = 1. Under this mode, the full adders receive Bx inputs in their complemented form and a 1 is added through the input carry Cin. Hence, the final output of the circuit is Ax + 2’s complement of Bx which is the subtraction of Ax and Bx.
这就是二进制加减器电路如何执行二进制加法和二进制减法运算的方式。
This is how the binary adder-subtractor circuit performs both binary addition and binary subtraction operations.
我们可以用以下几点总结二进制加减器的工作原理：
We can conclude the working of a binary adder-subtractor in the following points −
-
First of all, select the mode of operation (addition or subtraction) of the circuit. To perform binary addition, set M = 0, and to perform binary subtraction, set M = 1.
-
Supply the two input binary numbers to be added or subtracted.
-
The circuit will perform the addition or subtraction of input numbers depending on the selected mode and produce a result (either a sum or a difference).
Advantages of Binary Adder-Subtractor
在数字电路设计领域，重要的是尽可能地使电路紧凑。由于二进制加减器电路在单个电路中组合了二进制加法和减法运算。它导致以下关键优势 –
In the field of digital circuit design, it is important to make the circuit compact as much as possible. Since a binary adder-subtractor circuit combines both binary addition and subtraction operations in a single circuit. It results in the following key advantages −
-
Reduced circuit complexity
-
Compact and simpler system design
-
Versatility
-
Ability to perform fast and efficient arithmetic operations
-
Reduced need for hardware components
-
Compatibility with a wide range of digital systems and devices
-
Low power consumption, etc.
Limitations of Binary Adder-Subtractor
如上所列，二进制加减器具有许多优点。但它也有一些缺点和限制。
Binary adder-subtractor has several advantages as listed above. But it also has some disadvantages and limitations.
二进制加减器的一些主要限制列在下文 –
Some of the key limitations of binary adder-subtractor are listed below −
-
A binary adder-subtractor requires more advanced circuit components and algorithms to achieve high precision and accuracy in addition and subtraction operations.
-
The functionality of a binary adder-subtractor is limited to addition and subtraction operations only. It requires additional circuitry and algorithms to implement other mathematical operations like multiplication and division.
-
The circuit complexity of a binary adder-subtractor is increased significantly when it is designed to perform addition and subtraction of large numbers of bits and floating-point numbers.
-
When the number of digits increases in the numbers to be added or subtracted, the circuit becomes slower due to propagation delay.
-
A binary adder-subtractor has a limited dynamic range due to which overflow or underflow conditions can occur when dealing with very large or very small numbers respectively.
-
Since a binary adder-subtractor uses 2’s complement arithmetic to perform binary subtraction. To implement this operation, we require an additional logic circuit which increases the overall complexity of the circuit.
在设计二进制加减器时，我们必须考虑到所有这些限制，以确保电路的更高效率和更好的性能。
While designing a binary adder-subtractor, we have to take care of all these limitations to ensure higher efficiency and better performance of the circuit.
Applications of Binary Adder-Subtractor
在数字电子学中，二进制加减器在各种数字系统和电子设备中都有应用。以下列出了一些使用二进制加减器作为关键组件的常见设备 –
In digital electronics, the binary adder-subtractor finds applications in a variety of digital systems and electronic devices. Some common devices are listed below in which the binary adder-subtractor is used as a crucial component −
-
Arithmetic Logic Units − To perform arithmetic and logical operations.
-
Microprocessors and Microcontrollers − To perform mathematical computations.
-
Communication Systems − To process digital signals and filter operations on binary data.
-
Calculators − To perform addition and subtraction operations.
-
Control Systems − To perform real-time signal processing and produce feedback and other control signals.
Conclusion
在本章中，我们解释了二进制加法器-减法器的基本原理和工作原理。二进制加法器-减法器是一种数字电子电路，可以执行二进制数的加法和减法操作。它将两个算术运算（加法和减法）组合到一个电路中，从而降低了数字系统的电路复杂度和尺寸。
In this chapter, we explained the basic theory and working of binary adder-subtractor. A binary adder-subtractor is a digital electronic circuit that can perform both addition and subtraction of binary numbers. It combines two arithmetic operations (addition and subtraction) into a single circuit and hence reduces the circuit complexity and size of the digital system.
二进制加法器-减法器广泛用于各种数字系统和设备，例如微处理器、微控制器、计算器等。
Binary adder-subtractor are widely used in various digital systems and devices such as microprocessors, microcontrollers, calculators, and more.