Digital Teaching Aid (DED Philippinen, 86 p.) 
Fundamental Logic Operations  Lesson 1 

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: Speech  
B: Boardscript  
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. 11: 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. 12: Load line and circuit
for a transistor switch
Hard Saturation
To get hard saturation, a designer makes I_{C} approximately 10 times the value of I_{B}.
When the max. Vin equals to the supply voltage you can get hard saturation by using a ratio of:
10:1 for R_{B}/R_{C}
Inverter Function
A transistor switch (circuit as above) can be used to build the first device in digital electronic, the inverter:
Fig. 13: 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.
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. 14: Voltage levels for high
and low state in TTL
IC's
All decisions and operations can be realized by means of the three basic operations:
NOT, AND, OR
NOT (Inverter)
Fig. 15: 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. 16: 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. 16: 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. 18: 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. 19: 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. 110: Logic circuit with truth
table
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
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