Boolean logic
• data that is stored and processed in a computer needs to be in binary format.
• logic gate as the most basic building block of the computer.
An Introduction to
• The logic gate is an electronic circuit that normally consists of a number of transistors.
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
• These transistors are arranged in such a way that the logic gate performs a logic operation.
Digital Logic • The logic operation that is carried out by these gates is known as Boolean logic, developed by the
English mathematician George Boole.
How Signals and Integrated circuits work
1 2
Boolean Algebra Basic operations of Boolean algebra
• Boolean algebra has been fundamental in the development of digital electronics • NOT – reverses the value of the operand.
• Whereas in elementary algebra expressions denote mainly numbers, in Boolean • AND – results in TRUE if both operands are TRUE
algebra they denote the truth values (false and true).
• OR – results in TRUE if at least one of the operands is TRUE
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
• These values are represented with the bits (or binary digits), namely 0 and 1.
• XOR – results in TRUE if one (and only one) of the operands is TRUE (exclusive OR)
3 4
, NOT AND Operation
NOT operator AND operator
“NOT” operation: Changes a statement from TRUE to Output is TRUE, IF and only IF
A (input) C (output) FALSE and vice–versa, i.e. inversion A (input) B (input) C (output) both events are TRUE.
TRUE FALSE Therefore it is denoted as, TRUE TRUE TRUE Therefore it is denoted as,
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
C=A C=A.B (Boolean Expression)
FALSE TRUE TRUE FALSE FALSE
FALSE TRUE FALSE
FALSE FALSE FALSE
5 6
OR Operation XOR
OR operator XOR operator
Output is TRUE, IF at LEAST ONE Output is TRUE, IF AND ONLY IF
A (input) B (input) C (output) of the events are TRUE. A (input) B (input) C (output) ONE of the events are TRUE
TRUE TRUE TRUE Therefore it is denoted as, TRUE TRUE FALSE Therefore it is denoted as,
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
C=A+B (Boolean Expression) C = A⊕B (Boolean Expression)
TRUE FALSE TRUE TRUE FALSE TRUE
FALSE TRUE TRUE FALSE TRUE TRUE
FALSE FALSE FALSE FALSE FALSE FALSE
7 8
• data that is stored and processed in a computer needs to be in binary format.
• logic gate as the most basic building block of the computer.
An Introduction to
• The logic gate is an electronic circuit that normally consists of a number of transistors.
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
• These transistors are arranged in such a way that the logic gate performs a logic operation.
Digital Logic • The logic operation that is carried out by these gates is known as Boolean logic, developed by the
English mathematician George Boole.
How Signals and Integrated circuits work
1 2
Boolean Algebra Basic operations of Boolean algebra
• Boolean algebra has been fundamental in the development of digital electronics • NOT – reverses the value of the operand.
• Whereas in elementary algebra expressions denote mainly numbers, in Boolean • AND – results in TRUE if both operands are TRUE
algebra they denote the truth values (false and true).
• OR – results in TRUE if at least one of the operands is TRUE
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
• These values are represented with the bits (or binary digits), namely 0 and 1.
• XOR – results in TRUE if one (and only one) of the operands is TRUE (exclusive OR)
3 4
, NOT AND Operation
NOT operator AND operator
“NOT” operation: Changes a statement from TRUE to Output is TRUE, IF and only IF
A (input) C (output) FALSE and vice–versa, i.e. inversion A (input) B (input) C (output) both events are TRUE.
TRUE FALSE Therefore it is denoted as, TRUE TRUE TRUE Therefore it is denoted as,
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
C=A C=A.B (Boolean Expression)
FALSE TRUE TRUE FALSE FALSE
FALSE TRUE FALSE
FALSE FALSE FALSE
5 6
OR Operation XOR
OR operator XOR operator
Output is TRUE, IF at LEAST ONE Output is TRUE, IF AND ONLY IF
A (input) B (input) C (output) of the events are TRUE. A (input) B (input) C (output) ONE of the events are TRUE
TRUE TRUE TRUE Therefore it is denoted as, TRUE TRUE FALSE Therefore it is denoted as,
ELT2116/2216 - Computer Applications
ELT2116/2216 - Computer Applications
C=A+B (Boolean Expression) C = A⊕B (Boolean Expression)
TRUE FALSE TRUE TRUE FALSE TRUE
FALSE TRUE TRUE FALSE TRUE TRUE
FALSE FALSE FALSE FALSE FALSE FALSE
7 8
