Computer organization and Architecture
Unit-1
Computer Architecture
Computer Architecture refers to those attributes of a system that have a direct impact on the
logical execution of a program.
Examples:
● the instruction set
● the number of bits used to represent various data types
● I/O mechanisms
● memory addressing techniques
1. Computer Architecture is concerned with the way hardware components are connected
together to form a computer system.
2. It acts as the interface between hardware and software.
3. Computer Architecture helps us to understand the functionalities of a system.
4. A programmer can view architecture in terms of instructions, addressing modes and
registers.
5. While designing a computer system architecture is considered first.
6. Computer Architecture deals with high-level design issues.
7. Architecture involves Logic (Instruction sets, Addressing modes, Data types, Cache
optimization.
Computer Organization
Computer Organization refers to the operational units and their interconnections that realize the
architectural specifications. Examples are things that are transparent to the programmer:
● control signals
● interfaces between computer and peripherals
● the memory technology being used
1. Computer Organization is concerned with the structure and behavior of a computer
system as seen by the user.
2. It deals with the components of a connection in a system.
3. The Computer Organization tells us how exactly all the units in the system are arranged
and interconnected.
4. Whereas Organization expresses the realization of architecture.
5. An organization is done on the basis of architecture.
6. The Computer Organization deals with low-level design issues.
7. Organization involves Physical Components (Circuit design, Adders, Signals,
Peripherals)
,Boolean Algebra
● Boolean algebra was invented in 1854 by George boole.
● It uses only the binary numbers 0 1nd 1.
● It is used to analyze and simplify the digital (logic) circuits.
● It is also called Binary Algebra or logical Algebra.
● It is mathematics of digital logic
● A variable is a symbol usually represented with an uppercase letter
● Complement is the inverse of a variable; it can be denoted by a bar above the variable.
● A literal ia a variable or the complement of a variable.
● Boolean expressions are created by performing operations on Boolean variables. –
Common Boolean operators include AND, OR, and NOT
● OR operation between two variables denoted using plus (+) symbol (A OR B as A + B)
● AND operation between two variables denoted using dot (.) symbol (A AND B as A . B)
● NOT operation is a unary operation i.e. complement of a variable (NOT A as or A’ )
Duality Principle
According to this principle every valid boolean expression (equality) remains valid
if the operators and identity elements are interchanged.
In this principle,
● if we have theorems of Boolean Algebra for one type of operation then that operation
can be converted into another type of operation
● i.e., AND can be converted to OR and vice-versa
, ● interchange
'0 with 1',
'1 with 0',
'(+) sign with (.) sign' and
'(.) sign with (+) sign'.
● This principle ensures that if a theorem is proved using the theorem of Boolean algebra,
then the dual of this theorem automatically holds and we need not prove it again
separately. This is an advantage of dual principle.
● Some Boolean expressions and their corresponding duals are given below,
Example :
If boolean expression is
A.(B+C)=(A.B) + (A.C)
Then its dual expression is ,
A+(B.C)=(A+B).(A+C)
Boolean expression
It is an algebraic statement which contains variables and operators.
Theorems/axioms/postulates can also be proved using the truth table method. The other
method is by an algebraic manipulation using axioms/postulates or other basic theorems. Few
application of dual principle are as follows:
Idempotency Law
A) x + x = x
B) x . x = x
We will prove part A)
LHS = (x + x). 1 ----------------- Identity law
= (x + x).(x + x’) ----------------- Complement law
= x + x.x’ ----------------- Distributive law
= x + 0 ----------------- Complement law
= x ----------------- Identity law
= RHS
As part A is proved, according to dual principle we need not to prove
part B.
Absorption Law
A) x + (x . y) = x
B) x . (x + y) = x
We will prove part A)
LHS = x . 1 + x . y ----------------- Identity law
= x . ( 1 + y) ----------------- Distributive law
= x . (y + 1) ----------------- Commutative law
= x . 1 -----------------? (Identify the law) ______________
= x ----------------- Identity law
= RHS
As part A is proved, according to dual principle we need not to prove part B.
, Logic Gates
Video Link: https://www.youtube.com/watch?v=47u7b2yh7s8
Logic gates are the basic building blocks of digital systems. This electronic circuit has one or
more than one input and only one output.
● The logic gates are the main structural part of a digital system.
● Logic Gates are a block of hardware that produces signals of binary 1 or 0 when input
logic requirements are satisfied.
● Each gate has a distinct graphic symbol, and its operation can be described by means of
algebraic expressions.
● The seven basic logic gates include: AND, OR, XOR, NOT, NAND, NOR, and XNOR.
● The relationship between the input-output binary variables for each gate can be
represented in tabular form by a truth table.
● Each gate has one or two binary input variables designated by A and B and one binary
output variable designated by x.
AND Gate
It is a binary operation, it requires at least two inputs and generates one output.
The output of AND gate is High or On or 1 only if both the inputs are High or On
or 1, else for the rest of all cases the output is Low or off or 0.
Symbol
Y=A.B
OR Gate
It is a binary operation, it requires at least two inputs and generates one output.
The output of OR gate is Low or Off or 0 only if both the inputs are Low or Off or
0 , else for the rest of all cases the output is High or On or 1.
Unit-1
Computer Architecture
Computer Architecture refers to those attributes of a system that have a direct impact on the
logical execution of a program.
Examples:
● the instruction set
● the number of bits used to represent various data types
● I/O mechanisms
● memory addressing techniques
1. Computer Architecture is concerned with the way hardware components are connected
together to form a computer system.
2. It acts as the interface between hardware and software.
3. Computer Architecture helps us to understand the functionalities of a system.
4. A programmer can view architecture in terms of instructions, addressing modes and
registers.
5. While designing a computer system architecture is considered first.
6. Computer Architecture deals with high-level design issues.
7. Architecture involves Logic (Instruction sets, Addressing modes, Data types, Cache
optimization.
Computer Organization
Computer Organization refers to the operational units and their interconnections that realize the
architectural specifications. Examples are things that are transparent to the programmer:
● control signals
● interfaces between computer and peripherals
● the memory technology being used
1. Computer Organization is concerned with the structure and behavior of a computer
system as seen by the user.
2. It deals with the components of a connection in a system.
3. The Computer Organization tells us how exactly all the units in the system are arranged
and interconnected.
4. Whereas Organization expresses the realization of architecture.
5. An organization is done on the basis of architecture.
6. The Computer Organization deals with low-level design issues.
7. Organization involves Physical Components (Circuit design, Adders, Signals,
Peripherals)
,Boolean Algebra
● Boolean algebra was invented in 1854 by George boole.
● It uses only the binary numbers 0 1nd 1.
● It is used to analyze and simplify the digital (logic) circuits.
● It is also called Binary Algebra or logical Algebra.
● It is mathematics of digital logic
● A variable is a symbol usually represented with an uppercase letter
● Complement is the inverse of a variable; it can be denoted by a bar above the variable.
● A literal ia a variable or the complement of a variable.
● Boolean expressions are created by performing operations on Boolean variables. –
Common Boolean operators include AND, OR, and NOT
● OR operation between two variables denoted using plus (+) symbol (A OR B as A + B)
● AND operation between two variables denoted using dot (.) symbol (A AND B as A . B)
● NOT operation is a unary operation i.e. complement of a variable (NOT A as or A’ )
Duality Principle
According to this principle every valid boolean expression (equality) remains valid
if the operators and identity elements are interchanged.
In this principle,
● if we have theorems of Boolean Algebra for one type of operation then that operation
can be converted into another type of operation
● i.e., AND can be converted to OR and vice-versa
, ● interchange
'0 with 1',
'1 with 0',
'(+) sign with (.) sign' and
'(.) sign with (+) sign'.
● This principle ensures that if a theorem is proved using the theorem of Boolean algebra,
then the dual of this theorem automatically holds and we need not prove it again
separately. This is an advantage of dual principle.
● Some Boolean expressions and their corresponding duals are given below,
Example :
If boolean expression is
A.(B+C)=(A.B) + (A.C)
Then its dual expression is ,
A+(B.C)=(A+B).(A+C)
Boolean expression
It is an algebraic statement which contains variables and operators.
Theorems/axioms/postulates can also be proved using the truth table method. The other
method is by an algebraic manipulation using axioms/postulates or other basic theorems. Few
application of dual principle are as follows:
Idempotency Law
A) x + x = x
B) x . x = x
We will prove part A)
LHS = (x + x). 1 ----------------- Identity law
= (x + x).(x + x’) ----------------- Complement law
= x + x.x’ ----------------- Distributive law
= x + 0 ----------------- Complement law
= x ----------------- Identity law
= RHS
As part A is proved, according to dual principle we need not to prove
part B.
Absorption Law
A) x + (x . y) = x
B) x . (x + y) = x
We will prove part A)
LHS = x . 1 + x . y ----------------- Identity law
= x . ( 1 + y) ----------------- Distributive law
= x . (y + 1) ----------------- Commutative law
= x . 1 -----------------? (Identify the law) ______________
= x ----------------- Identity law
= RHS
As part A is proved, according to dual principle we need not to prove part B.
, Logic Gates
Video Link: https://www.youtube.com/watch?v=47u7b2yh7s8
Logic gates are the basic building blocks of digital systems. This electronic circuit has one or
more than one input and only one output.
● The logic gates are the main structural part of a digital system.
● Logic Gates are a block of hardware that produces signals of binary 1 or 0 when input
logic requirements are satisfied.
● Each gate has a distinct graphic symbol, and its operation can be described by means of
algebraic expressions.
● The seven basic logic gates include: AND, OR, XOR, NOT, NAND, NOR, and XNOR.
● The relationship between the input-output binary variables for each gate can be
represented in tabular form by a truth table.
● Each gate has one or two binary input variables designated by A and B and one binary
output variable designated by x.
AND Gate
It is a binary operation, it requires at least two inputs and generates one output.
The output of AND gate is High or On or 1 only if both the inputs are High or On
or 1, else for the rest of all cases the output is Low or off or 0.
Symbol
Y=A.B
OR Gate
It is a binary operation, it requires at least two inputs and generates one output.
The output of OR gate is Low or Off or 0 only if both the inputs are Low or Off or
0 , else for the rest of all cases the output is High or On or 1.
