number system

1. Number System in Digital Electronics
Prof. Neeraj Bhargava
Pooja Dixit
Department of Computer Science,
School of Engineering & System
Sciences
MDS University Ajmer, Rajasthan

2. • Definition: In digital electronics, the number system is used for representing the
information.
• The number system has different bases (radix) and the most common of them are the
decimal, binary, octal, and hexadecimal.
• Suppose if the number system representing the digit from 0 – 9 then the base
of the system is the 10.
• Types of Number Systems
Some of the important types of number system are
▫ Decimal Number System (Base 10)
▫ Binary Number System (Base 10)
▫ Octal Number System (Base 10)
▫ Hexadecimal Number System (Base 10)
What are Number System?

3. What are Number System?
1. Binary Number Systems
• It uses only two digits 0 and1.The base of binary number system is 2 because it has only
two digit 0 and 1.
• The digital electronic equipments are works on the binary number system
and hence the decimal number system is converted into binary system.
• Note: 1 Byte= 8 Bit
• 1 Bit=4 Nibble
• Examples:
• (10100)2, (11011)2, (11001)2, (000101)2, (011010)2.
2. Decimal Number Systems
• The number system is having digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; this number system is known
as a decimal number system because total ten digits are involved. The base of the decimal
number system is 10.

4. What are Number System?
3. Octal Number System
• The octal number system has base 8(means it has only eight digits from
0 to 7).
• There are only eight possible digit values to represent a number. With
the help of only three bits, an octal number is represented. Each set of
bits has a distinct value between 0 and 7.
• Examples:
• (273)8, (5644)8, (0.5365)8, (1123)8, (1223)8.
Number Octal Number
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

5. What are Number System?
4. Hexadecimal Number System
• The number system has a base of 16 means there are total 16 symbols (0, 1, 2, 3, 4, 5, 6, 7,
8, 9, A, B, C, D, E, F) used for representing a number.
• The single-bit representation of decimal values10, 11, 12, 13, 14, and 15 are represented by
A, B, C, D, E, and F.
• Only 4 bits are required for representing a number in a hexadecimal number.
• Examples:
• (FAC2)16, (564)16, (0ABD5)16, (1123)16, (11F3)16.
Binary Number Hexadecimal Number
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

6. Number Base Conversion

7. Number Base Conversion
1. Binary to Decimal Conversion
• The process of converting binary to decimal is quite simple. The process
starts from multiplying the bits of binary number with its corresponding
positional weights. And lastly, we add all those products.
• Let's take an example to understand how the conversion is done from binary
to decimal.
• Ex: 10101

8. Number Base Conversion
1. Ex: 111012
• Binary Number − 111012 = Decimal Number − 2910
Step Binary Number Decimal Number
Step
1
111012 ((1 × 2
4
) + (1 × 2
3
) + (1 × 2
2
) + (0 × 2
1
) + (1 × 2
0
))10
Step
2
111012 (16 + 8 + 4 + 0 + 1)10
Step
3
111012 2910

9. Binary to Decimal Conversion for Fractional Number
• Ex: .0101

10. • Example 1: (10110.001)2
• We multiplied each bit of (10110.001)2 with its
respective positional weight, and last we add the
products of all the bits with its weight.
• (10110.001)2=(1×24)+(0×23)+(1×22)+(1×21)+(0×20)+
(0×2-1)+(0×2-2)+(1×2-3)
(10110.001)2=(1×16)+(0×8)+(1×4)+(1×2)+(0×1)+
(0×1⁄2)+(0×1⁄4)+(1×1⁄8)
(10110.001)2=16+0+4+2+0+0+0+0.125
(10110.001)2=(22.125 )10

11. Binary to Decimal Conversion For Mixed Number
Ex: 1101.101
After disregarding the weight 21 and 2-1 and on summing up the
remaining weights the required decimal number is 13.625.

12. Questions
convert the following binary numbers to decimal equivalents:
A, 001100
B, 000011
C, 011100
D, 111100
E, 111111
Solutions: