Computer Organisation and Architecture Unit-2
Number System
The language we use to communicate with each other is comprised of words and characters.
We understand numbers, characters and words. But this type of data is not suitable for
computers. Computers only understand the numbers.
So, when we enter data, the data is converted into electronic pulse. Each pulse is identified as
code and the code is converted into numeric format by ASCII. It gives each number, character
and symbol a numeric value (number) that a computer understands. So to understand the
language of computers, one must be familiar with the number systems.
The Number Systems used in computers are:
● Binary number system
● Octal number system
● Decimal number system
● Hexadecimal number system
1. Binary number system
It has only two digits '0' and '1' so its base is 2. Accordingly, In this number system, there
are only two types of electronic pulses; absence of electronic pulse which represents
'0'and presence of electronic pulse which represents '1'. Each digit is called a bit. A
group of four bits (1101) is called a nibble and group of eight bits (11001010) is called a
byte. The position of each digit in a binary number represents a specific power of the
base (2) of the number system.
Binary to Decimal
Binary to Octal
, Binary to Hexa Decimal
2. Octal number system
It has eight digits (0, 1, 2, 3, 4, 5, 6, 7) so its base is 8. Each digit in an octal number
represents a specific power of its base (8). As there are only eight digits, three bits
(23=8) of binary number system can convert any octal number into binary number. This
number system is also used to shorten long binary numbers. The three binary digits can
be represented with a single octal digit.
Octal to Binary
Octal to Decimal
Octal to Hexa Decimal
3. Decimal number system
This number system has ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) so its base is 10. In this
number system, the maximum value of a digit is 9 and the minimum value of a digit is 0.
The position of each digit in decimal number represents a specific power of the base (10)
, of the number system. This number system is widely used in our day to day life. It can
represent any numeric value.
Convert the following:
1. Convert to Binary - 30 118, 593, 35.60, 828.90
2. Convert to Octal - 1972, 52, 456
3. Convert to HexaDecimal - 3000, 450.50, 336.27
4. HexaDecimal Number System
This number system has 16 digits that ranges from 0 to 9 and A to F. So, its base is 16.
The A to F alphabets represent 10 to 15 decimal numbers. The position of each digit in a
hexadecimal number represents a specific power of base (16) of the number system. As
there are only sixteen digits, four bits (24=16) of binary number system can convert any
hexadecimal number into binary number. It is also known as alphanumeric number
system as it uses both numeric digits and alphabets.
Hexadecimal to Binary
Hexadecimal to Decimal
Hexa Decimal to Octal
Number System
The language we use to communicate with each other is comprised of words and characters.
We understand numbers, characters and words. But this type of data is not suitable for
computers. Computers only understand the numbers.
So, when we enter data, the data is converted into electronic pulse. Each pulse is identified as
code and the code is converted into numeric format by ASCII. It gives each number, character
and symbol a numeric value (number) that a computer understands. So to understand the
language of computers, one must be familiar with the number systems.
The Number Systems used in computers are:
● Binary number system
● Octal number system
● Decimal number system
● Hexadecimal number system
1. Binary number system
It has only two digits '0' and '1' so its base is 2. Accordingly, In this number system, there
are only two types of electronic pulses; absence of electronic pulse which represents
'0'and presence of electronic pulse which represents '1'. Each digit is called a bit. A
group of four bits (1101) is called a nibble and group of eight bits (11001010) is called a
byte. The position of each digit in a binary number represents a specific power of the
base (2) of the number system.
Binary to Decimal
Binary to Octal
, Binary to Hexa Decimal
2. Octal number system
It has eight digits (0, 1, 2, 3, 4, 5, 6, 7) so its base is 8. Each digit in an octal number
represents a specific power of its base (8). As there are only eight digits, three bits
(23=8) of binary number system can convert any octal number into binary number. This
number system is also used to shorten long binary numbers. The three binary digits can
be represented with a single octal digit.
Octal to Binary
Octal to Decimal
Octal to Hexa Decimal
3. Decimal number system
This number system has ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) so its base is 10. In this
number system, the maximum value of a digit is 9 and the minimum value of a digit is 0.
The position of each digit in decimal number represents a specific power of the base (10)
, of the number system. This number system is widely used in our day to day life. It can
represent any numeric value.
Convert the following:
1. Convert to Binary - 30 118, 593, 35.60, 828.90
2. Convert to Octal - 1972, 52, 456
3. Convert to HexaDecimal - 3000, 450.50, 336.27
4. HexaDecimal Number System
This number system has 16 digits that ranges from 0 to 9 and A to F. So, its base is 16.
The A to F alphabets represent 10 to 15 decimal numbers. The position of each digit in a
hexadecimal number represents a specific power of base (16) of the number system. As
there are only sixteen digits, four bits (24=16) of binary number system can convert any
hexadecimal number into binary number. It is also known as alphanumeric number
system as it uses both numeric digits and alphabets.
Hexadecimal to Binary
Hexadecimal to Decimal
Hexa Decimal to Octal
