The document discusses various number systems, including decimal, binary, hexadecimal, and octal, detailing their bases and digit compositions. It explains how to convert binary numbers to decimal using positional values and demonstrates binary arithmetic operations such as addition, subtraction, multiplication, and division with examples for each. Additionally, it provides step-by-step examples for computing binary arithmetic, illustrating the processes involved.

1. Made By:-
Ananya Goel
VII-C
Roll No. 07

2. Types Of Number Systems
• Commonly used number system.
• Consists of 10 digits (0-9). Base-10
• Example:-107, 78, 98, 2786
Decimal
Number System
• Used in digital computers.
• Consists of 2 digits (0 and 1). Base-2
• Example:-100101,001010
Binary Number
System
• Consists of 16 digits [ (0-9) and (A-F) ]
• Base – 16
• Example:- D1CE, 2E6
Hexadecimal
Number System
• Consists of 8 digits ( 0-7 )
• Base – 8
• Example:-6675,453,655
Octal Number
System

4.  Multiply each Binary number with its positional value, which is in terms
of powers of 2, starting from the extreme right digit.
 Increase the power one by one, keeping the Base fixed as 2.
 Sum up all products to get the Decimal Number.
Example – Convert (1001)₂ in Decimal Number.
T H T U
(1 0 0 1)₂
1 × 2⁰ = 1
0 × 2 = 0 The sum is = 1 + 0 + 0 + 8 = 9
0 × 2² = 0 Therefore, (1001)₂ = (9) ₁₀
1 × 2³ = 8

5. A B A + B = C
0 0 0 + 0 = 0
0 1 0 + 1 = 1
1 0 1 + 0 = 1
1 1 1 + 1 = 10
Example – Compute (11111)₂ + (1011)₂
1 1 1 1 Carry Over
1 1 1 1 1
0 1 0 1 1
1 0 1 0 1 0 Therefore, (11111)₂ + (1011)₂
= (101010)₂

6. A B A - B = C
0 0 0 – 0 = 0
1 0 1 – 0 = 1
1 1 1 – 1 = 0
0 1 0 – 1 = 1
(With a borrow taken from
next place i.e., 10-1=1)
Example :- Compute (1100)₂ - (1011)₂
10 -1 = 1
1 1Borrowed 1 0 1
- 1 0 1 1 The answer is = (0010)₂
0 0 1 0

7. A B A * B = C
0 0 0 * 0 = 0
0 1 0 * 1 = 0
1 0 1 * 0 = 0
1 1 1 * 1 = 1
Example- Compute (101)₂ × (11)₂
101
× 11
101
+ 101×
1111 Therefore, the answer is (1111)₂

8. The method to perform division of two Binary Numbers is same
as that of Decimal Numbers.
Example- Compute (110)₂ ÷ (10)₂
1 1 Quotient
1 0 1 1 0 Dividend
1 0
0 1 0
1 0
0 0 Remainder