What is Binary?

• Binary numbers use only two digits: 0 and 1.
• Computers use binary because their circuits can be ON (1) or OFF (0).
• Each place in a binary number represents a power of 2 (like 1, 2, 4, 8, 16…).

Part 1: How to Convert a Decimal Number to Binary (Step-by-Step)

Let’s start with the decimal number 13 and change it into binary.

Step 1: Divide the number by 2

• Take the number (13) and divide it by 2.
• Write down the remainder (what’s left over after division).

Step 2: Write down the remainder

• If the number divides evenly, the remainder is 0.
• If not, the remainder will be 1.

Step 3: Divide the result (quotient) by 2 again

• Ignore the remainder for this step, only divide the quotient.
• Repeat Steps 1 and 2.

Step 4: Keep dividing until you get zero as the quotient

Step 5: Write all the remainders from bottom to top

This is your binary number!

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Example with number 13:

Step	Divide	Quotient	Remainder
1	13 ÷ 2	6	1
2	6 ÷ 2	3	0
3	3 ÷ 2	1	1
4	1 ÷ 2	0	1

Write remainders from bottom to top: 1101

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Part 2: How to Convert Binary to Decimal (Step-by-Step)

Now, let’s change binary 1101 back to a decimal number.

Step 1: Write the binary digits in a row

• Start from the right (last digit).

Step 2: Assign powers of 2 starting from 0

Binary digit	Power of 2
1	2⁰ = 1
0	2¹ = 2
1	2² = 4
1	2³ = 8

Step 3: Multiply each binary digit by its power of 2

• Multiply the digit (0 or 1) by the power of 2 value.

Step 4: Add all the results together

• This is your decimal number!

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Example with binary 1101:

Digit	Power of 2	Multiply (Digit × Power)
1	8	1 × 8 = 8
1	4	1 × 4 = 4
0	2	0 × 2 = 0
1	1	1 × 1 = 1

Add them all: 8 + 4 + 0 + 1 = 13

Why Should Beginners Learn This?

• Binary numbers are how computers understand data.
• Knowing this helps you in programming, digital electronics, and exams.
• It’s a simple skill that opens up new ways of thinking about numbers!