Digital Teaching Aid (DED Philippinen, 86 p.)
 Fundamental Logic Operations - Lesson 1
 Lesson Plan Handout No. 1 Worksheet No. 1

### (introduction...)

Titel: Fundamental Logic Operations

Objectives:

- Understand the principle of NOT, AND, OR operations
- Able to convert binary and decimal numbers

 Time Method Topic Way Remark S,D * Introduction Ex - Analog and digital signals S,Q/A * Review B -Transistor in hard saturation - Inverter function S,D *TTL circuits B -History - Standards S * Logic operations B S,E -NOT HO Handout No. 1 (Family of TTL devices) S,E -AND EX S,E -OR EX E * Binary number system WS Worksheet No. 1 S: SpeechD: DiscussionQ/A: Question/AnswerE: Exercise B: BoardscriptP: PictureEx: ExampleHO: Hands-OnWS: WorksheetHT: Hand-Out

### Introduction

Fundamental Logic Operations

Digital Electronics

The world of electronics is divided into two areas: analog and digital. Analog circuits consist mainly of amplifiers for voltage or current variations that are smooth and continuous. Digital circuits provide electronic switching of voltage pulses. A pulse has abrupt changes between two extreme amplitude levels (i.e.: 5 volt = high level and 0 volt = low level).

Since the digital signal has only two significant levels, either high or low, it is useful to represent the pulses in a binary number system with the digits 1 and 0. (see also Worksheet 1, Binary number system)

Fig. 1-1: Analog versus digital signals

Transistor in digital electronic

A transistor can be used in analog and digital electronic. In digital electronic the transistor operates usually in hard saturation. (see also Amplifier Teaching Aid, Transistor as switch)

Fig. 1-2: Load line and circuit for a transistor switch

Hard Saturation

To get hard saturation, a designer makes IC approximately 10 times the value of IB.

When the max. Vin equals to the supply voltage you can get hard saturation by using a ratio of:

10:1 for RB/RC

Inverter Function

A transistor switch (circuit as above) can be used to build the first device in digital electronic, the inverter:

Fig. 1-3: Inverter symbol and truth table

Because in digital electronics mainly ready made devices are used (Integrated circuits IC), we don't care any more how the single device is built up. From now on we will use only these ready made devices.

### TTL circuits

1964 TEXAS Instruments introduced a family of digital devices which became standard elements in digital electronic: The TTL (Transistor Transistor Logic) circuits. The High (1) and Low (1) state is represented by voltage levels.

Fig. 1-4: Voltage levels for high and low state in TTL IC's

### Logic operations

All decisions and operations can be realized by means of the three basic operations:

NOT, AND, OR

NOT (Inverter)

Fig. 1-5: NOT (Inverter) symbol and truth table

Circuit example: 7404 TTL device (see Handout No. 1)

HO: A 1KHz square wave drives pin 1 of a 7404. What does the voltage waveform at pin 2 look like?

Solution:

Fig. 1-6: Timing diagram, Inverter input (pin 1) and output (pin 2)

AND gates

AND operation: The output supplies an high (1) signal if to all inputs high (1) signals are applied.

Fig. 1-6: AND symbol and truth table

AND application example: An elevator motor may only start to work if the doors are shut AND an operation occured.

Circuit example: TTL device 7408, two input AND gate

Ex: Develop the truth table for the following logic circuit.

Fig. 1-8: Logic circuit with truth table

OR gates

OR operation: An OR operation supplies a high signal at the output if to one or more inputs high signals are applied.

Fig. 1-9: OR gate, symbol and truth table

OR application example: A pump has to be switched on when the water level has fallen to a certain level OR too much water is taken out of the container.

Circuit example: TTL device 7432, two input OR gate

Ex: Develop the truth table for the following logic circuit.

Fig. 1-10: Logic circuit with truth table

### Handout No. 1

The 7400 Family of TTL Devices (Sample List)

 Device number Description 7400 Quad 2 input NAND gates 7402 Quad 2 input NOR gates 7404 Hex inverter 7408 Quad 2 input AND gates 7410 Triple 3 input NAND gates 7411 Triple 3 input AND gates 7427 Triple 3 input NOR gates 7432 Quad 2 input OR gates

Figure

### Worksheet No. 1

Binary number system

All number systems have a base, which specifies how many digits can be used in each place count. For binary numbers the base is 2, with 0 and 1 as the only two digits. In the decimal system, the base is 10.

Decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Binary digits: 0, 1

Decimal to Binary Conversion

EX: Convert a 4 bit binary number (100 1) into decimal.

Each digit position has specified weight, for binary numbers the position represents a power of two.

EX: Convert a 8 bit number (10010101) into decimal

HO: Convert the following binary numbers into decimal:

101, 1100, 1110, 1000, 0110, 11001010, 01101111, 10001100

Binary to decimal conversion

EX: Convert the decimal number 138 into a binary number

HO: Convert the following decimal numbers into binary numbers:

12, 8, 127, 247, 139, 255