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Feature Decimal Number System Binary Number System
Base System Base 10 Base 2

Digits Used Uses ten digits (0 to 9) Uses two digits (0 and 1)
Each digit's position is a power of Each bit's position is a power of 2
Positional Weights
10 (e.g., 10², 10¹, 10⁰) (e.g., 2⁵, 2⁴, 2³, etc.)
Most Significant Digit/Bit Leftmost digit; highest place value Leftmost bit; highest power of 2
(MSD/MSB)
Least Significant Digit/Bit Rightmost digit; smallest place Rightmost bit; smallest power of 2
(LSD/LSB) value
Used for everyday counting, Used for digital computing and
Usage Context
money, measurements electronic devices
110100=(1×2⁵ + 1×2⁴ + 0×2³ + 1×2²
Example 724=(7×10² + 2×10¹ + 4×10⁰)
+ 0×2¹ + 0×2⁰)

CONVERSIONS BETWEEN NUMBER SYSTEMS

Computers use the binary number system (0s and 1s), but people usually use the decimal number
system (digits 0 to 9). So, sometimes we need to change numbers from one system to the other. This
is called conversion.

Converting Decimal to Binary

To convert a decimal number into a binary number, follow these steps:
Divide the decimal number by 2 (the base of the binary number system).

Note down the quotient and remainder.
Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.

Repeat the procedure until the quotient is less than 2.

List the last quotient and all the remainders (moving from bottom to top). You will get your binary
number.
Look at the given examples to understand the conversion better.

Example 1: Convert the decimal number 26, i.e., (26) to binary.
10
2 26

2 13 → 0
2 6 → 1

2 3 → 0
1 → 1
Start listing the last quotient and all the remainders from here.

The binary equivalent of (26) is 11010
10
In other words, (26) = (11010) 2
10

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