Digital Electronics
DIGITAL ELECTRONICS
Number System:
A number system is defined as a system of writing to express numbers. A number system is a
mathematical system with base n, where n represents total numbers present in that system.
Eg: In decimal number system, the number of digits is 10
Radix Point:
Radix point is a base point used to separate the integer part and the fractional part of a number.
Base or radix:
The number of symbols used in a number system is called base or radix of the number system.
Eg: In decimal number system – Base is 10
In Binary number system – Base is 2
In Hexadecimal number system – Base is 16 etc.
Most significant bit (MSB):
The left most bit of a binary number which has the highest place value is called most significant bit.
Least significant bit (LSB):
The right most bit of a binary number which has the least place value is called least significant bit.
Bit:
A binary digit is called a bit.
Example: 0 or 1
Nibble:
A group of four bits is called a Nibble.
Example: 0110, 1110 etc.
Byte:
A group of eight bits is called a byte.
Example: 01101101, 11010011 etc.
Types of number systems
Binary number system
Octal number system
Decimal number system
Hexadecimal number system
Binary number system:
The base of binary number system is 2. The digits used are 0 and 1.
Example: 11001(2), 0101(2)
Octal number system:
The base of octal number system is 8.
The digits used are 0, 1, 2, 3, 4, 5, 6 and 7.
Example: 157(8), 2312(8), 110(8)
Table representing decimal, Octal and binary number
Decimal Number Octal Number Binary Number
0 0 000
1 1 001
2 2 010
3 3 011
4 4 100
5 5 101
6 6 110
7 7 111
Decimal number system:
The base of decimal number system is 10.
The digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Example: 0157(10), 6587(10), 0110(10)
Hexadecimal number system:
The base of hexadecimal number system is 16.
The digits used are 0, 1, 2, 3, 4, 5, 6, 7, 8 9, A, B, C, D, E and F.
Example: 0157(16), 2312(16), 0110(16), ABC5(16), BDEF(16)
Table representing decimal, hexadecimal and binary number
Decimal Number Hexadecimal Number Binary Number
0 0 0000
1 1 0001
2 2 0010
3 3 0011
4 4 0100
5 5 0101
6 6 0110
7 7 0111
8 8 1000
9 9 1001
10 A 1010
11 B 1011
12 C 1100
13 D 1101
14 E 1110
15 F 1111
Binary Arithmetic
Binary arithmetic includes the basic arithmetic operations of addition, subtraction, multiplication
and division
Binary Addition: The rules to perform binary addition are
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 with a carry 1
Binary Subtraction: The rules to perform binary subtraction are
0 – 0 = 0
0 – 1 = 1 with a borrow 1
1 – 0 = 1
1 – 1 = 0
Binary Multiplication: The rules to perform binary multiplication are
0 X 0 = 0
0 X 1 = 0
1 X 0 = 0
1 X 1 = 1
Binary Division: The rules to perform binary division are
0 ÷ 0 = not defined
0 ÷ 1 = 0
1 ÷ 0 = not defined
1 ÷ 1 = 1
1’s Complement of binary numbers:
The 1’s complement of a binary number is obtained by changing each 0 to 1 and 1 to 0.
Eg: The 1’s complement of (101101)2 is (010010)2
2’S Complement of binary numbers: The 2’S complement of a binary number is obtained by adding
1 to the 1’s complement of the number.
Eg: The 2’s complement of (101101)2 is (010010)2 + 1 = (010011)2
Note: The 1’S complement and the 2’S complement of a binary number help to do the subtraction by
the method of addition