Lecture 1 Digital Logic Circuit

第一课 数字逻辑电路

Exercises

• Please read the text and complete the exercises in 20 minutes.

1.Answer the following questions according to the text.• What are the three basic types of digital logic gates?——The AND gate, the OR gate, and the NOT gate.• How can the digital operation be achieved?——By using voltage pulses.• The digital circuit usually operates on two different

simple states, what are they?——1 state and 0 state.

• Write out the mathematic equation of the AND gate.

——A · B=C• Try to describe the function of the OR gate.

——The output of an OR gate is true if any one of the inputs is true and is false if all of the inputs are false.

2.Translate the following phrases and expressions.• two different voltage levels

—— 两种不同的电压状态• The closed-switch state can be represented by 1

—— 闭合的开关状态由 1 表示• be achieved by using voltage pulses

—— 通过电压脉冲来实现• solid-state transducers

—— 晶体管放大器

• The complementary metal oxide semiconductor logic (CMOC)

—— 互补型金属氧化物半导体逻辑• a large scale digital system

—— 大规模数字系统• 触发器——flip-flop• 数字逻辑电路——digital logic circuit

3.Choose the best answer.• The pulse is composed of _____ states.

A. One B. three C. two• The simplest way for the operation of a digital circuit

is made up of _____.

A. the closing of a switch

B. the opening of a switch

C. both A and B

C

C

• If voltage pulses are used in digital operation, the presence of a pulse can be represented by _____.

A. 1 B. 0 C. 2• “input A or input B equals output C” the statement

can be expressed by the equation _____ .

A. AB=C B. A + B=C C. AB=C• The AND gate, OR gate, NOT gate are the three basic

______.

A. flip-flops B. logic gates C. equation

A

B

B

4.Judge true or false according to the text.• In digital logic circuits, “true” can be represented by

1 and “false” by a 0.( )• The output of an OR gate is true only if all the inputs

are true.( )• An INVERTER has two or more inputs and a single

output.( )• Any analog function can be performed by the three

basic gates.( )

T

F

F

F

5.Translate the following sentences into English.• 在逻辑电路中数字“ 0” 和“ 1” 代表着两种不同

电压的信号。——In logic circuit ,1 and 0 appear as signals of two

different voltages.

——In logic circuit, signals of two different voltages can be represented by 1 and 0.

• 在二进制系统中 110 表示十进制的 6 。——In binary system 6 which is decimal is expressed

by 110.

• 数字逻辑门分成三种类型：与门、或门、非门。——Digital logic gates are sorted three types: the AND

gate, the OR gate, and the NOT gate.

• 任何复杂的逻辑电路均是由基本逻辑门组成的。——Any complicated logic circuits are built up from

elementary gates.

Key words and Technical terms

• digital electronics 数字电子学• system 系统，体系——circuit system, digital system• voltage level 电压状态• binary states 二进制状态• digital operation 数字运算• pulse 脉搏，脉冲——voltage pulse, positive pulse, negative pulse• square-wave signal 方波信号

• positive 肯定的，积极的；正的；阳的• negative 否定的，消极的；负的；阴性的• digital logic 数字逻辑• rational process 推理过程• rules of Boolean algebra 布尔代数定律• numeral 数字• mechanical switch 机械开关• transducer 传感器，变频器，变换器• solid-state transducer 晶体管放大器

• various families of 不同系列的• “OR”, “ AND”, and “NOT” gate

或门、与门、非门• transistor 晶体管• transistor-transistor logic (TTL) TTL 逻辑电路• complementary metal oxide semiconductor (CMOS)

互补型金属氧化物半导体• digital logic gate 数字逻辑门• inverter 反相器

• elementary/basic gate 基本逻辑门• control system 控制系统• digital-communication system 数字通信系统• flip-flop 触发器

Expressions

• consist of… 由…组成——They can, in the simplest form, consist of the

opening and closing of a switch.

——The United Kingdom consists of Great Britain and Northern Ireland.

• be achieved by … 通过…完成——A very common method of digital operation is

achieved by using voltage pulses.

——The dream of champion is achieved by his unremitting efforts.

• base on 基于——Digital logic is a rational process for making

simple “true” or “false” decisions based on the rules of Boolean algebra.

——The boss forgave his breach of duty this time based on his previous contribution to the company.

• be expressed by … 由…表示——The operation of an AND gate is mathematically

expressed by the equation A·B=C.——Logic function in digital circuit is usually

expressed by truth table, logic function expression, logic diagram and Karnaugh map.

Core Sentences Translation

• The two different states by which digital circuits operate may be of several forms.

—— 数字电路工作的两种状态可能呈现几种形式。• The closed-switch state can be represented by 1 and

the open-switch state by 0.

—— 闭合的开关状态由 1 表示，断开的状态由 0 表示。

• The presence of a positive pulse can be represented by 1 and the absence of a pulse by 0.

—— 用 1 表示正脉冲的到来，用 0 表示无脉冲。

• With a square-wave signal, the positive pulses can be represented by 1 and the negative pulses can be represented by 0.

—— 对于方波信号，用 1 表示正脉冲，用 0 表示负脉冲。

• “True” can be represented by a 1 and “false” by a 0, and in logic circuits the numerals appear as signals of two different voltages.

——“ 真”用 1 表示，“假”用 0 表示，且在逻辑电路中这两个数字代表着两种不同电压的信号。

• The various families of digital logic devices, usually integrated circuits, perform a variety of logic functions through logic gates.

—— 不同系列的数字逻辑器件（通常是集成电路）通过逻辑门电路来执行各种不同的逻辑功能。

• The three basic types of digital logic gates are the AND gate, the OR gate and the NOT gate.

—— 有三种基本类型的数字逻辑门——与门、或门和非门。

• The output of an AND gate is true only if all the inputs are true.

—— 只有当与门的输入均为真时其输出才为真。• The output of an OR gate is true if any one of the

inputs is true and is false if all of the inputs are false.—— 若输入中有一个为真，则或门的输出即为真；

或所有的输入均为假，则输出也为假。• An inverter has a single input and a single output

terminal and can change a true signal to a false signal, thus performing the NOT function.

—— 反相器仅有一个单独的输入端和一个输出端，能将真信号变换为假信号从而执行“非”功能。

• More complicated logic circuits are built up from elementary gates.

—— 更为复杂的逻辑电路均由基本的逻辑门构成。• Even in a large scale digital system, such as a

computer, control, digital-communication system, there are only a few basic operations, which must be performed.

—— 即使在诸如计算机、控制系统和数字通信系统这样的大规模数字系统中，也只是必须执行一些基本的运算。

Supplementary Information

What is “gates” and Boolean algebra?

• Digital circuits contain hardware elements called “gates” that perform logic operations on binary numbers.

– Devices such as transistors can be used to perform the logic operations.

• Boolean algebra is a mathematical system that provides the basis for these logic operations.

• The term Boolean variable is used to mean the two-valued binary digit 1 or 0.

• Boolean algebra uses three basic logic operations namely, NOT, OR, and AND.

NOT Operation• The NOT operation inverts or provides the one’s complement

of a binary digit.

• This operation takes a single input and generates one output.

• The NOT operation of a binary digit provides the following result:

NOT 1= 0

NOT 0= 1

• A NOT gate is also referred to as an “inverter” because it inverts the voltage levels.

• Ａ transistor acts as an inverter.

• A 0-volt at the input generates a 5-volt output; a 5-volt input provides a 0-volt output.

OR operation• The OR operation for two variables A and B generates a result

of 1 if A or B, or both, are 1. However, if both A and B are zero, then the result is 0.

• A plus sign + (logical sum) or symbol is normally used to ∨represent OR.

• The four possible combinations of ORing two binary digits are

0 + 0= 0

0 + 1= 1

1 + 0= 1

1 + 1= 1

• The diode is a switch, and it closes when there is a voltage drop of 0.7 V between the anode and the cathode.

• Suppose that a voltage range of 0 to 2 V is considered as logic 0 and a voltage of 3 to 5 V is logic 1.

• If both A and B are at logic 0 (say 1.5 V) with a voltage drop across the diodes of 0.7 V to close the diode switches, a current flows from the inputs through R to ground, and the output C will be at 1.5 V - 0.7 V = 0.8 V (logic 0). On the other hand, if one or both inputs are at logic 1 (say 4.5 V) the output C will be at 4.5V - 0.7 V = 3.8 V (logic 1).

• Therefore, the circuit acts as an OR gate.

AND operation• The AND operation for two variables A and B generates a

result of 1 if both A and B are 1.

• However, if either A or B, or both, are zero, then the result is 0. The dot and symbol are both used to represent the AND ∧operation. The AND operation between two binary digits is

0 · 0 = 0

0 · 1 = 0

1 · 0 = 0

1 · 1 = 1• As we did for the OR gate, let us assume that the range 0 to

+2V represents logic 0 and the range 3 to 5 V is logic 1.

• Now, if A and B are both HIGH (say 3.3 V) and the anode of both diodes at 4.0 V, the switches in D1 and D2 close.

• A current flows from +5 V through resistor R to +3.3 V input to ground. The output C will be HIGH (4.0 V).

• On the other hand, if a low voltage (say 0.5 V) is applied at A and a high voltage (3.3V) is applied at B. The value of R is selected in such a way that 1.2 V appears at the anode side of D1 at the same time 4.0 V appears at the anode side of D2.

• A current flows from the +5V input through R and the diodes to ground. Output C will be low (1.2 V) because the output will be lower of the two voltages. Thus, it can be shown that when either one or both inputs are low, the output is low, so the circuit works as an AND gate.