Boolean Logic | Computer Science for Grade 11 PDF Download

 Page 1


Boolean Logic
What does a Computer 
Understands
Computers do not understand natural
languages nor programming languages.
They only understand the language of
bits. A bit is the most basic unit in
computer machine language. All
instructions that the computer executes
and the data that it processes is made up
of a group of bits. Bits are represented in
many forms either through electrical
voltage, current pulses, or by the state of
an electronic flip-flop circuit in form of 0
or 1.
1 Bit = Binary Digit(0 or 1)
8 Bits = 1 Byte
1024 Bytes = 1 KB (Kilo Byte)
1024 KB = 1 MB (Mega Byte)
1024 MB = 1 GB(Giga Byte)
1024 GB = 1 TB(Terra Byte)
1024 TB = 1 PB(Peta Byte)
1024 PB = 1 EB(Exa Byte)
1024 EB = 1 ZB(Zetta Byte)
1024 ZB = 1 YB (Yotta Byte)
1024 YB = 1 (Bronto Byte)
1024 Brontobyte = 1 (Geop Byte)
Page 2


Boolean Logic
What does a Computer 
Understands
Computers do not understand natural
languages nor programming languages.
They only understand the language of
bits. A bit is the most basic unit in
computer machine language. All
instructions that the computer executes
and the data that it processes is made up
of a group of bits. Bits are represented in
many forms either through electrical
voltage, current pulses, or by the state of
an electronic flip-flop circuit in form of 0
or 1.
1 Bit = Binary Digit(0 or 1)
8 Bits = 1 Byte
1024 Bytes = 1 KB (Kilo Byte)
1024 KB = 1 MB (Mega Byte)
1024 MB = 1 GB(Giga Byte)
1024 GB = 1 TB(Terra Byte)
1024 TB = 1 PB(Peta Byte)
1024 PB = 1 EB(Exa Byte)
1024 EB = 1 ZB(Zetta Byte)
1024 ZB = 1 YB (Yotta Byte)
1024 YB = 1 (Bronto Byte)
1024 Brontobyte = 1 (Geop Byte)
Boolean Logic
Because of computer understands machine
language(0/1) which is binary value so every operation
is done with the help of these binary value by the
computer.
George Boole, Boolean logic is a form of algebra in
which all values are reduced to either 1 or 1.
To understand boolean logic properly we have to
understand Boolean logic rule,Truth table and logic
gates
Boolean Logic
Page 3


Boolean Logic
What does a Computer 
Understands
Computers do not understand natural
languages nor programming languages.
They only understand the language of
bits. A bit is the most basic unit in
computer machine language. All
instructions that the computer executes
and the data that it processes is made up
of a group of bits. Bits are represented in
many forms either through electrical
voltage, current pulses, or by the state of
an electronic flip-flop circuit in form of 0
or 1.
1 Bit = Binary Digit(0 or 1)
8 Bits = 1 Byte
1024 Bytes = 1 KB (Kilo Byte)
1024 KB = 1 MB (Mega Byte)
1024 MB = 1 GB(Giga Byte)
1024 GB = 1 TB(Terra Byte)
1024 TB = 1 PB(Peta Byte)
1024 PB = 1 EB(Exa Byte)
1024 EB = 1 ZB(Zetta Byte)
1024 ZB = 1 YB (Yotta Byte)
1024 YB = 1 (Bronto Byte)
1024 Brontobyte = 1 (Geop Byte)
Boolean Logic
Because of computer understands machine
language(0/1) which is binary value so every operation
is done with the help of these binary value by the
computer.
George Boole, Boolean logic is a form of algebra in
which all values are reduced to either 1 or 1.
To understand boolean logic properly we have to
understand Boolean logic rule,Truth table and logic
gates
Boolean Logic
Boolean Logic rules
Boolean Algebra is
the mathematics we
use to analyse digital
gates and circuits. We
can use these “Laws
of Boolean” to both
reduce and simplify a
complex Boolean
expression in an
attempt to reduce
the number of logic
gates required.
Boolean Expression Boolean Algebra Law or Rule
A + 1 = 1 Annulment
A + 0 = A Identity
A . 1 = A Identity
A . 0 = 0 Annulment
A + A = A Idempotent
A . A = A Idempotent
NOT A = A Double Negation
A + A = 1 Complement
A . A = 0 Complement
A+B = B+A Commutative
A.B = B.A Commutative
A+B = A.B de Morgan’s Theorem
A.B = A+B de Morgan’s Theorem
Boolean Logic
Page 4


Boolean Logic
What does a Computer 
Understands
Computers do not understand natural
languages nor programming languages.
They only understand the language of
bits. A bit is the most basic unit in
computer machine language. All
instructions that the computer executes
and the data that it processes is made up
of a group of bits. Bits are represented in
many forms either through electrical
voltage, current pulses, or by the state of
an electronic flip-flop circuit in form of 0
or 1.
1 Bit = Binary Digit(0 or 1)
8 Bits = 1 Byte
1024 Bytes = 1 KB (Kilo Byte)
1024 KB = 1 MB (Mega Byte)
1024 MB = 1 GB(Giga Byte)
1024 GB = 1 TB(Terra Byte)
1024 TB = 1 PB(Peta Byte)
1024 PB = 1 EB(Exa Byte)
1024 EB = 1 ZB(Zetta Byte)
1024 ZB = 1 YB (Yotta Byte)
1024 YB = 1 (Bronto Byte)
1024 Brontobyte = 1 (Geop Byte)
Boolean Logic
Because of computer understands machine
language(0/1) which is binary value so every operation
is done with the help of these binary value by the
computer.
George Boole, Boolean logic is a form of algebra in
which all values are reduced to either 1 or 1.
To understand boolean logic properly we have to
understand Boolean logic rule,Truth table and logic
gates
Boolean Logic
Boolean Logic rules
Boolean Algebra is
the mathematics we
use to analyse digital
gates and circuits. We
can use these “Laws
of Boolean” to both
reduce and simplify a
complex Boolean
expression in an
attempt to reduce
the number of logic
gates required.
Boolean Expression Boolean Algebra Law or Rule
A + 1 = 1 Annulment
A + 0 = A Identity
A . 1 = A Identity
A . 0 = 0 Annulment
A + A = A Idempotent
A . A = A Idempotent
NOT A = A Double Negation
A + A = 1 Complement
A . A = 0 Complement
A+B = B+A Commutative
A.B = B.A Commutative
A+B = A.B de Morgan’s Theorem
A.B = A+B de Morgan’s Theorem
Boolean Logic
Boolean Expression
A Boolean expression is a logical statement that is either 
TRUE or FALSE .
A Boolean expression can consist of Boolean data, such as the following:
* BOOLEAN values (YES and NO, and their synonyms, ON and OFF, and TRUE 
and FALSE)
* BOOLEAN variables or formulas
* Functions that yield BOOLEAN results
• BOOLEAN values calculated by comparison operators. E.g.
1. $F(x, y, z) = x' y' z' + x y' z + x y z' + x y z 
2. $F' (x, y, z) = x' y z + x' y' z + x' y z' + x y' z‘
3. $F(x, y, z) = (x + y + z) . (x+y+z') . (x+y'+z) . (x'+y+z)
Boolean Logic
Page 5


Boolean Logic
What does a Computer 
Understands
Computers do not understand natural
languages nor programming languages.
They only understand the language of
bits. A bit is the most basic unit in
computer machine language. All
instructions that the computer executes
and the data that it processes is made up
of a group of bits. Bits are represented in
many forms either through electrical
voltage, current pulses, or by the state of
an electronic flip-flop circuit in form of 0
or 1.
1 Bit = Binary Digit(0 or 1)
8 Bits = 1 Byte
1024 Bytes = 1 KB (Kilo Byte)
1024 KB = 1 MB (Mega Byte)
1024 MB = 1 GB(Giga Byte)
1024 GB = 1 TB(Terra Byte)
1024 TB = 1 PB(Peta Byte)
1024 PB = 1 EB(Exa Byte)
1024 EB = 1 ZB(Zetta Byte)
1024 ZB = 1 YB (Yotta Byte)
1024 YB = 1 (Bronto Byte)
1024 Brontobyte = 1 (Geop Byte)
Boolean Logic
Because of computer understands machine
language(0/1) which is binary value so every operation
is done with the help of these binary value by the
computer.
George Boole, Boolean logic is a form of algebra in
which all values are reduced to either 1 or 1.
To understand boolean logic properly we have to
understand Boolean logic rule,Truth table and logic
gates
Boolean Logic
Boolean Logic rules
Boolean Algebra is
the mathematics we
use to analyse digital
gates and circuits. We
can use these “Laws
of Boolean” to both
reduce and simplify a
complex Boolean
expression in an
attempt to reduce
the number of logic
gates required.
Boolean Expression Boolean Algebra Law or Rule
A + 1 = 1 Annulment
A + 0 = A Identity
A . 1 = A Identity
A . 0 = 0 Annulment
A + A = A Idempotent
A . A = A Idempotent
NOT A = A Double Negation
A + A = 1 Complement
A . A = 0 Complement
A+B = B+A Commutative
A.B = B.A Commutative
A+B = A.B de Morgan’s Theorem
A.B = A+B de Morgan’s Theorem
Boolean Logic
Boolean Expression
A Boolean expression is a logical statement that is either 
TRUE or FALSE .
A Boolean expression can consist of Boolean data, such as the following:
* BOOLEAN values (YES and NO, and their synonyms, ON and OFF, and TRUE 
and FALSE)
* BOOLEAN variables or formulas
* Functions that yield BOOLEAN results
• BOOLEAN values calculated by comparison operators. E.g.
1. $F(x, y, z) = x' y' z' + x y' z + x y z' + x y z 
2. $F' (x, y, z) = x' y z + x' y' z + x' y z' + x y' z‘
3. $F(x, y, z) = (x + y + z) . (x+y+z') . (x+y'+z) . (x'+y+z)
Boolean Logic
De Morgan’s Law
The complement of the union of two sets is equal to the
intersection of their complements and the complement
of the intersection of two sets is equal to the union of
their complements. These are called De Morgan’s laws.
For any two finite sets A and B
(i) (A U B)' = A' n B' (which is a De Morgan's law of union).
OR
(A+B)’=A’.B’
(ii) (A n B)' = A' U B' (which is a De Morgan's law of intersection).
OR
(A . B)’=A’+B’
Boolean Logic