### Binary, Octal and Hexadecimal Systems

Describe positional notation and manually convert numbers between different bases (2, 8, 10, and 16)

Binary number system:
0000 = 0
0001 = 1
0010 = 2
0011 = 3
0100 = 4
0101 = 5
0110 = 6
0111 = 7
1000 = 8
1001 = 9
1010 = 10
1011 = 11
1100 = 12
1101 = 13
1110 = 14
1111 = 15
Octal Number System:
Octal number system has a base of 8 : (0,1,2,3,4,5,6,7)
Hexadecimal numbers are made of 16 digits, it uses the digits 0 through 9 plus the letters A, B, C, D, E, F.

### Solved Example:

#### 9922-01

Which among the following are basic numbers that are used in Binary Numerical System? (MP Vyapam Sub Engineer Sep. 2018 shift I Mechanical)

### Solved Example:

#### 9922-02

A-F system is used in which of the following number systems? (UGC NET Sep 2020 Shift II)

### Solved Example:

#### 9922-03

Computer uses which number system to store data and perform calculations? (UGC NET Jun 2019 Shift II

### Solved Example:

#### 9922-04

Given below are two statements

Statement I: The base of the binary number system is 2.

Statement II: Binary addition is just like decimal addition except that the rules are much simpler.

(UGC NET Paper I: Nov 2021 Shift II)

In light of the above statements, choose the correct answer from the options given below