Digital-electronics 简明教程
Difference between Half Adder and Full Adder
加法器电路是计算机、计算器、数字处理单元等中使用的重要数字电路之一。加法器电路有两种类型，分别命名为 half-adder 和 full-adder 。半加法器和全加法器电路均用于执行加法，并且广泛用于在数字电路中执行各种算术函数。
An adder circuit is one of the important digital circuits used in computers, calculators, digital processing units, etc. There are two types adder circuits named half-adder and full-adder. Both the half adder and the full adder circuits are used to perform addition and also widely used for performing various arithmetic functions in the digital circuits.
What is a Half Adder?
用来对两个二进制数字求和的组合逻辑电路称为 half adder 。半加法器提供输出以及进位值（如果有的话）。半加法器电路是通过连接一个 EX-OR 门和一个 AND 门来设计的。它有两个输入端子和两个用于和与进位的输出端子。
A combinational logic circuit which is designed to add two binary digits is known as half adder. The half adder provides the output along with a carry value (if any). The half adder circuit is designed by connecting an EX-OR gate and one AND gate. It has two input terminals and two output terminals for sum and carry.
在半加法器的情况下，EX-OR 门的输出是两个位的和，而 AND 门的输出是进位。然而，在下次加法中不会转发本次加法获得的进位，因此称为半加法器。
In case of half adder, the output of the EX-OR gate is the sum of two bits while the output of the AND gate is the carry. However, the carry obtained is one addition will not be forwarded in the next addition, so it is called half adder.
半加法器的输出方程为：
The output equations of the half adder are −
\mathrm{Sum, \: S \: = \: A \oplus{B}}
\mathrm{Carry, \: C \: = \: A\cdot B}
What is a Full Adder?
用来对三个二进制数字求和并产生两个输出的组合电路称为全加法器。 full adder 电路对三个二进制数字求和，其中两个是输入，另一个是前一次加法进位的进位。
A combinational circuit which is designed to add three binary digits and produce two outputs is known as full adder. The full adder circuit adds three binary digits, where two are the inputs and one is the carry forwarded from the previous addition.
全加法器的电路包括两个 EX-OR 门、两个 AND 门和一个 OR 门，它们相互连接，如全加法器电路中所示。
The circuit of the full adder consists of two EX-OR gates, two AND gates and one OR gate, which are connected together as shown in the full adder circuit.
全加法器的输出方程为：
The output equations of the full adder are −
\mathrm{Sum, \: S \: = \: A \oplus{B} \oplus{C_{in}}}
\mathrm{进位， \: C \: = \: AB \: + \: BC_{in} \: + \: AC_{in}}
\mathrm{Carry, \: C \: = \: AB \: + \: BC_{in} \: + \: AC_{in}}
Difference Between Half Adder and Full Adder
下表展示了半加法器和全加法器电路之间的主要差异。
The following table shows the main differences between half adder and full adder circuit.
Parameter |
Half Adder |
Full Adder |
Definition |
Half adder is a combinational digital circuit which can add two 1-bit binary numbers. |
Full adder is a combinational digital circuit which can add three single-bit binary number, where two are the inputs and the third is the carry forwarded from the previous output. |
Circuit components |
The circuit of the half adder consists of one EX-OR gate and one AND gate. |
The circuit of full adder consists of two EX-OR gates, two AND gates and one OR gate. |
Addition of carry bit |
The half adder does not add the carry generated in the previous addition to the next addition. |
In case of full adder, the carry produced in the previous addition is added in the next addition. |
Number of input and output terminals |
Half adder circuit has two input terminals viz. A and B and two output terminals, viz. Sum and Carry. |
Full adder circuit has three input terminals viz. A, B and Cin and two output terminals, i.e., Sum and Carry. |
Logical Expressions |
For half adder circuit, the logical expressions of the outputs are − $\mathrm{S \: = \: A \oplus{B}}$ $\mathrm{C \: = \: A\cdot B} $ |
For full adder circuit, the logical expressions of the outputs are − $\mathrm{S \: = \: A \oplus{B} \oplus{C_{in}}}$ $\mathrm{C \: = \: AB \: + \: BC_{in} \: + \: AC_{in}}$ |
Substitution |
A half adder circuit cannot be used as a full adder circuit. |
A full adder circuit can substitute a half adder circuit. |
Design |
The circuit of a half adder is simple and easy to implement. |
The circuit of a full adder has relatively complex design. |
Alternate Name |
For half adder, there is no alternate name. |
Full adder is also called ripple-carry adder. |
Applications |
Half adder circuits are used in computers, calculators, and various digital measuring instruments. |
Full adders are mainly used for multiple bit addition, in digital processing devices, etc. |
Conclusion
从上述讨论中清楚地看出，半加器电路和全加器电路之间有几个不同之处。然而， half adder 和 full adder 电路都是许多数字电路的基本构建模块，这些电路可用于执行算数运算，例如计算机、计算器、数字测量装置、数字处理器等。
From the above discussion, it is clear that there are several differences between a half-adder circuit and a full-adder circuit. However, both half adder and full adder circuits are the basic building blocks of many digital circuits that are used to perform arithmetic operations such as calculators, computers, digital measuring devices, digital processors, etc.
在数字电路中使用半加器和全加器的主要好处之一是，它们采用逻辑门来设计，可以非常快速地处理输入数据。逻辑门的典型处理速度是 μs（微秒）的数量级。因此，为了以高速执行算数运算，我们使用半加器和全加器电路。
One of the main advantage of using half adders and full adders in the digital circuits is that they are designed by using logic gates that process the input data very fast. The typical processing speed of the logic gates is of the order of μs (microseconds). Hence, for performing arithmetic operations at high speed, we use half adder and full adder circuits.