Part II - Boolean logic
in computing, electrical engineering, mathematics, English…
Boolean algebra
George Boole, an English mathematician, is the inventor of Boolean logic, known today as
Boolean Algebra, which is the basis of modern digital computer logic. Therefore Boole is
regarded as a founder of the field of computer science.
A set of rules formulated by Boole describe certain propositions whose outcome would be
either true or false. With regard to digital logic, these rules are used to describe circuits whose
state can be either, 1 (true) or 0 (false). In order to fully understand this, the relation between
the AND, OR and NOT operations should be appreciated.
Binary system
Today, all our computers use Boole's logic system - using microchips that contain thousands
of tiny electronic switches arranged into logical ‘gates’ that produce predictable and reliable
conclusions.
The basic logic gates are AND, OR, NOT, NAND and NOR. It is these gates, used in
different combinations, that allow the computer to execute its operations using binary
language.
Binary numbers are closely related to digital electronics. With digital electronics a ‘1’ means
that current / electricity is present and a ‘0’ means it is not present. Different parts of a
computer communicate through voltage pulses (1s and 0s). Computers can calculate complex
equations and perform complex mathematics at lightening speed. Calculating using only 1s
and 0s is called the binary logic.
Digital electronic circuit design
Boolean logic is also used for circuit design in electrical engineering. Logic circuits assess
information (consisting of high (1) or low (0) voltages) and produce a single high or low
voltage logical conclusion. Every possible input-output behaviour can be modelled by a
suitable Boolean expression. The voltage itself represents the binary yes-no, true-false, onezero concept. Digital electronic circuit usually consists of several logic gates that are logically
connected and represent the combinational logic.
English language use of Boolean terms
An English sentence can also be converted into a formal Boolean statement.
AND and OR can also be used interchangeably in English, in certain cases:
o "I always carry an umbrella for when it rains and snows."
o "I always carry an umbrella for when it rains or snows."
o "I never walk in the rain or snow."
I. Complete the sentences.
1. Boolean algebra was ……………………….…….by George Boole.
2. Boolean logic is based on ……………………… system.
3. Logic gates are the……………………………… of digital electronics.
Sources:
http://en.wikipedia.org/wiki/George_Boole
http://en.wikipedia.org/wiki/Boolean_logic#cite_note-0
http://en.wikipedia.org/wiki/Logic_gates
© Marija Šubic, prof.
http://www.kerryr.net/pioneers/binary.htm
http://www.kerryr.net/pioneers/boolean.htm
http://www.technologystudent.com/elec1/biny1.htm
PROJEKTNI TEDEN
Part II
II. Which logic gate am I?
A
B
Y
A
B
Y
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
………….
………….
A
0
0
1
1
B
0
1
0
1
Y
A
B
Y
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
………….
………….
III. Look at the picture and answer.
1. What do these acronyms stand for?
GND
Vcc
V
&
2. Which logic gates have been used?
3. In which IC the IEC symbols have been used?
4. In which IC the ANSI symbols have been used?
AND / OR / NAND / NOR
A/B
A/B
IEC - International Electrochemical Commission
ANSI - American National Standards Institute
What does ISO stand for?
IV. HOMEWORK
Interactive exercise – LOGIC GATES
http://www2.arnes.si/~sspmsubi/GATES1.htm
*V. Simplifying Boolean Algebra - VIDEO
Boolean Operators - VIDEO
Boolean Algebra – Ppt Presentation
© Marija Šubic, prof.
PROJEKTNI TEDEN
Part II