What Are Combinational Logic Circuits?

Digital circuits can be divided into two categories according to the different characteristics of logic functions, one is called combinational logic circuit (combined circuit for short), and the other is called sequential logic circuit (sequential circuit for short). The logic function of the combinational logic circuit is that the output at any time depends only on the input at that time, and has nothing to do with the original state of the circuit. The logic function of the sequential logic circuit is that the output at any time depends not only on the input signal at that time, but also on the original state of the circuit, or it is related to the previous input.

Chinese name: Combinational logic circuit
Foreign name: combinational logic circuit

Pinyin: z hé luó ji diàn lù
Complex: Combinational logic circuit

Combination logic circuit principle

Combination logic circuit means that at any time, the output state is determined only at the same time.

Combinational logic circuit The combination of input states has nothing to do with the previous state of the circuit and has nothing to do with the state at other times. Its logical function is as follows:

Li = f (A1, A2, A3 ... An) (i = 1, 2, 3 ... m)

Among them, A1 ~ An are input variables and Li is output variable.

The characteristics of combinational logic circuits are summarized as follows:

There is no feedback delay channel between input and output;

There is no memory unit in the circuit.

For the first logic expression formula or logic circuit, its truth table can be unique, but its corresponding logic circuit or logic expression may have multiple implementation forms. Therefore, for a specific logic problem, its corresponding truth value The table is unique, but the logic circuits that implement it are diverse. In actual design work, if some gate circuits cannot be obtained for some reasons, you can change the circuit by changing the logic expression, so that other devices can be used instead of the device. At the same time, in order to make the design of the logic circuit more concise, it is necessary to simplify the logic expression through various methods. A combinational circuit can be described by a set of logical expressions. Designing a combination circuit is all about implementing logical expressions. It is required that on the basis of satisfying logic functions and technical requirements, there are various ways to make the circuit simple, economical, and reliable, and to implement the combined logic function. Basic gate circuits can also be used, and medium and large-scale integrated circuits can also be used. The general design steps are:

Analyze design requirements and list truth tables;

Perform logic and necessary transformations. Get the simplest logical expression needed;

Draw a logic diagram.

Combinational logic circuit analysis

In the asic design and pld design, the simplest combination of logic circuit design is very important, and it is often required to use the least number of logic gates or wires to implement the design. In asic design and pld design, a large number of constraint terms need to be processed, but terms with a value of 1 or 0 are limited. A new method for designing combinational logic circuits is proposed.

AND logic means that the result will only occur if all the conditions that determine the result of the thing are met. The combination of all factors of a certain combination of output variables 1 and the combination of output variables 1 appears, and all the combinations of output variables 0 do not appear, so the combination of output variables 1 can be represented. The analysis of combinational logic circuit is divided into the following steps:

(1) Have a given logic circuit diagram, write the logical expression at the output;

(2) List truth tables;

(3) Summarize the logic function through the truth table to see if the original circuit is optimal, and if not, improve it.

Combinational logic circuits

Combination logic circuit arithmetic operation circuit

1. Half and full adders

Half adder

The two numbers A and B are added together, and only the sum of the bases is calculated.

The logic circuit that completes the half-add function is called a half-adder. When binary addition is actually performed, the two addends are generally not one bit, so the half adder without taking into account the low-order carry cannot solve the problem ^[1] .

Full adder

Adding two numbers not only considers the sum of the bases, but also considers the carry digits from the lower digits. The logic circuit that realizes this function is called full adder ^[1] .

2. Adder

A circuit that performs multi-bit binary number addition is called an adder. Depending on the carry method, there are two types of serial carry adder and super carry adder ^[1] .

Four-bit serial adder: such as T692. Advantages: simple circuit and easy connection. Disadvantages: The operation speed is not high. The calculation of the most significant bit must wait until all the low-order bits are completed in accordance with this operation, and then the carry signal can be sent. In order to increase the operation speed, the super look-ahead method can be adopted ^[1] .

Super carry-forward adder: The so-called super-carry forward is that during the addition operation, the carry signal of each digit is directly generated from the input binary number ^[1] .

Combination logic circuit encoder

1. basic concept

The process of expressing a specific signal with a code is called coding; the logic circuit that implements the coding function is called an encoder. The input of the encoder is the encoded signal, and the output is a set of binary codes corresponding to the input signal ^[1] .

2. Ordinary encoder

Three-bit binary encoder: Binary encoder: When n-bit binary code is used, a circuit that encodes m = 2n general signals ^[1] .

Binary Decimal Encoder: A circuit that encodes 0-9 decimal digits into binary code. There are 2n kinds of n-bit binary codes, which can encode m2n signals. Since the input of a two-digit decimal encoder is ten decimal numbers, a four-digit binary code representation system should be used. Ten of 2n = 16 binary codes are used to represent 0-9. This is a decimal number. There are many schemes. The most commonly used is 8421BCD code. In the two-decimal encoder, the input signals representing 0-9 are also mutually exclusive. Its working principle and design process are exactly the same as those of the three-bit binary encoder, and are not repeated ^[1] .

3 Priority encoder

Definition: Allow several signals to be input at the same time, but only encode the signal with the highest priority among them, and ignore the signal with lower priority. Such a circuit is called a priority encoder ^[1] .

Combination logic circuit decoder

1. basic concept

Definition: The process of converting the binary code to the corresponding output signal is called decoding. The logic circuit that completes the decoding function is called a decoder. The n inputs and m outputs of the decoder should satisfy 2nm. Decoders include binary decoders, binary-decimal decoders, and digital display decoders ^[1] .

2. Binary decoder

The various states of the binary code are converted into corresponding signal outputs according to their original intention. This circuit is called a binary decoder. In a binary decoder, if the input code has n bits, the output signal is 2n. So it can translate the entire state of the input variable. (Sometimes called the variable decoder, or the minimum term generator ^[1] .

Combination logic circuit data selector

Function: Select one channel as output from several input signals. There are many varieties of domestic data selectors: T4157, T4158, T4257, T4258, etc. are four-digit, two-to-one, one-selector; T4352, T4353, etc., four-to-one, one-to-one; T1150 and so on are 1 in 16. CMOS products are: CC4512 is 1 in 8 and CCI4539 is 1 in 4 and so on ^[1] .

Combination logic circuit data distributor

1. Data distributor logic function

The data demultiplexer (Demultiplexer) is also called a multiplexer. It has only one data input terminal, but has 2n data output terminals. According to the different combinations of n selection inputs, the data is sent to one of the 2n data output terminals. From its role, it is very similar to multi-position switches. From the perspective of logic functions, it is exactly the opposite of the data selector ^[1] .

2. Using a decoder as a data distributor

Any decoder with an enable control end can be used as a data distributor ^[1] .

3 Multiplex signal time-sharing

The combination of a data selector and a data distributor can realize time-sharing transmission of multiple signals. Principle: When the input C2C1C0 = 001 is selected, the data selector sends the state of XIN1 to the output. For the data distributor, it is to distribute the XIN1 sent to the XOUT1 terminal. The signals are not transmitted at the same time, but the transmission line is reduced ^[1] .

Combined logic circuit numerical comparator

1.1-bit numerical comparator

When comparing two 1-bit binary numbers, there are 4 possibilities and 3 results. ^[1]

2. Multi-bit value comparator

Let: A = A ₃ A ₂ A ₁ A ₀ , B = B ₃ B ₂ B ₁ B ₀

Use l _i = 1 to indicate A _i > B _i ;

m _i = 1, which means A _i < B _i ;

g _i = 1 means A _i = B _i .

When comparing, you should start from high. If the high bit compares with the result, you don't need to compare the low bit. When the high-order bits are equal, the low-order bits are compared ^[1] .

Combination logic circuit design

General steps:

(1) List truth tables from practical logic issues;

(2) Write a logical expression from the truth table;

(3) Simplify and transform the output logical expressions;

(4) Draw a logic diagram.

Combination logic circuit operation unit

In digital systems, arithmetic operations are performed using addition, so the adder is the most basic arithmetic unit in digital systems. Since binary operations can be represented by logical operations, logic circuits can be used to design arithmetic circuits. Addition is divided into full add and half add in the digital system, so the adder is also divided into full adder and half adder.

Design of Combination Logic Circuit Half Adder

The half adder does not consider the carry from the low bit to the local bit, so it has two inputs and two outputs.

Let the addend (input end) be A, B; and S be; the carry to the high position is Ci + 1

The logical expression of the function is: S = AB + AB; Ci + 1 = AB + 1

Design of Full Adder for Combination Logic Circuit

Because the full adder considers carry from low to high, it has three inputs and two outputs.

Truth Table and Full Adder Let the input variables (addenda) A, B, Ci-1, and the output variables S, Ci + 1

The logical expression of the function is: S = ABCi-1 + ABCi-1 + ABCi-1 + ABCi-1 = ABCi-1

Ci + 1 = ABCi-1 + ABCi-1 + ABCi-1 + ABCi-1 = (AB) Ci-1 + AB

Application of Combiner Logic Full Adder

Because the adder is the most basic logic device in digital systems, it is widely used. It can be used for binary subtraction, multiplication, BCD code addition and subtraction, code group conversion, digital comparison, etc.

Combining logic circuit coding and decoding

The process of specifying a binary code to represent a particular signal is called encoding. The process of translating the specific meaning of a group of binary codes is called decoding.

Encoder (1) Encoder Because n-bit binary digits have 2 ^ n states, it can represent 2 ^ n sets of information. In the coding process, people generally use coding matrices and coding tables. The coding matrix is to specify each square on the Carnot diagram to represent a certain natural number, and fill these natural numbers into the corresponding squares.

Decoder The inverse process of encoding is decoding. Decoding is the generation

decoder The code is translated into a certain output signal to indicate its original intention. The circuit that implements the decoding is the decoder. Decoders can be divided into binary decoders, decimal decoders, integrated decoders, and digital display decoding drive circuits. Among them, the binary decoder is the simplest variable decoder, and its output end is the smallest term.

Combination logic circuit selector

Data selector

The data selector selects one output from multiple inputs, which is equivalent to a multiplexer. Commonly used are one of two choices, one of four choices, one of eight choices, and one of sixteen choices. If more is needed, the above extensions will be made.