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Example 2: (16) = (?)
10 2

2 16 Learn More
2 8  0
2 4  0 Gottfried Leibniz invented
2 2  0 the modern binary number
1  0 system.

 1

(16) = (10000)
10 2
Conversion of Binary Number System into Decimal Number System

Following are the steps that need to be followed to convert binary number system into decimal
number system.
Step 1: Multiply each digit with its positional value, which is in terms of power of 2, starting
from the extreme right digit.

Step 2: Increase the power one by one, keeping the Think and Discuss
base fi xed at 2.

Step 3: Add all the products to get the decimal number. Which number system do we use?
Let’s understand with the help of examples.

Example 1: (1 0 0 1) = (?) 10 Example 2: (1 0 1 0) = (?) 10
2
2
1 × 2 0 = 1 0 × 2 0 = 0

0 × 2 1 = 0 1 × 2 1 = 2

0 × 2 2 = 0 0 × 2 2 = 0
3
3
1 × 2 = 8 1 × 2 = 8
9 10

(1001) = (9) (1010) = (10)
2 10 2 10
Octal Number System

The octal number system consists of 8 digits, i.e., 0 to 7 digits. Hence, the base of octal number
system is 8. Some examples of octal number system are 527 and 45.

Conversion of Octal Number System into Decimal Number System

Following are the steps that need to be followed for converting octal number system into
decimal number system.

Step 1: Multiply each digit with its positional value, which is in terms of powers of 8, starting
from the extreme right digit.

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