What is Binary?

 

🔢 Binary → Decimal (Very Easy Explanation)

🔹 Step-1: What is Binary?

Binary number uses only two digits:

0 and 1

Example binary numbers:

1011
110
1001

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🔹 Step-2: Powers of 2 (MEMORY TRICK)

Start from right side.

Position	Power of 2
1st (rightmost)	2⁰ = 1
2nd	2¹ = 2
3rd	2² = 4
4th	2³ = 8
5th	2⁴ = 16

👉 Just double each time

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🔹 Step-3: Rule (Very Simple)

👉 Multiply each binary digit by its power of 2
👉 Add all results

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✅ Example-1 (Very Simple)

Convert 1011₂ to Decimal

Write powers under digits:

Binary :   1   0   1   1
Power  :  2³  2²  2¹  2⁰
Value  :   8   4   2   1

Now multiply:

1 × 8 = 8
0 × 4 = 0
1 × 2 = 2
1 × 1 = 1

Add them:

8 + 0 + 2 + 1 = 11

✅ Final Answer:

1011₂ = 11₁₀

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✅ Example-2 (More Easy)

Convert 110₂ to Decimal

Binary :  1   1   0
Power  : 2²  2¹  2⁰
Value  :  4   2   1

Multiply & add:

1×4 + 1×2 + 0×1
= 4 + 2 + 0
= 6

✔ 110₂ = 6₁₀

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✅ Example-3 (Only 1 digit)

Convert 1₂ to Decimal

1 × 2⁰ = 1 × 1 = 1

✔ 1₂ = 1₁₀

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✅ Example-4 (With Zeroes)

Convert 1001₂ to Decimal

Binary :   1   0   0   1
Power  :  2³  2²  2¹  2⁰
Value  :   8   4   2   1

Multiply:

1×8 = 8
0×4 = 0
0×2 = 0
1×1 = 1

Add:

8 + 1 = 9

✔ 1001₂ = 9₁₀

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🧠 Super Easy Shortcut (EXAM FRIENDLY)

👉 Just remember this table

Binary	Decimal
1	1
10	2
11	3
100	4
101	5
110	6
111	7
1000	8

Exam questions often come from here 👆

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❓ Common Exam Trick Question

Q: Binary 0001 equals?

• Leading zeros don’t matter
  ✔ Answer = 1

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🎯 One-Line Memory Rule

Start from right → multiply by 1, 2, 4, 8 → add