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Base Systems
Base Systems · 6 Sections

Binary, Octal & Hexadecimal

Understand how computers count, convert between bases, and master the shortcuts that make base-system questions easy.

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Section 1 of 6

🏗️ What is a Number Base?

When we write the number 237, we instinctively know it means 2 hundreds, 3 tens, and 7 ones. That intuition comes from the base-10 (decimal) system — we use 10 distinct digit symbols (0–9) and the value of each position is a power of 10.

Key ideaIn a base-N system, there are exactly N valid digit symbols (0 through N−1), and each position to the left is worth N times the position to its right.

Computers use base-2 (binary) because transistors have two states: on and off. Programmers use base-16 (hexadecimal) as a compact way to write binary data. Base-8 (octal) appears in Unix file permissions and older computing contexts.

SystemBaseValid Digits
Binary20, 1
Octal80 – 7
Decimal100 – 9
Hexadecimal160–9, A–F

Notice that in base-8, the digit 8 does not exist — just as in base-10 the digit 10 does not exist as a single symbol. When you run out of symbols, you carry over to the next position.

We write a subscript to show the base: 101₂ = binary, 37₈ = octal, 1F₁₆ = hexadecimal, 42₁₀ = decimal.

Quick check — which of the following is a valid binary number?
📝Practice Questions

Q1How many distinct digit symbols does the octal (base-8) system use?

Q2Which of the following is NOT a valid hexadecimal digit?

Q3The number 10 in base-5 equals which decimal value?

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Section 2 of 6

🔟 Decimal System (Base 10)

Complete section 1 above to unlock this section.

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Section 3 of 6

🔵 Binary System (Base 2)

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Section 4 of 6

8️⃣ Octal System (Base 8)

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Section 5 of 6

🔣 Hexadecimal System (Base 16)

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Section 6 of 6

⚡ Conversions & Shortcuts

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Every Question Type — Solved

9 question types · 18 solved examples from real SSC papers

The six lessons above built the concepts. This gallery shows the exact question shapes that appear in SSC exams — one tap reveals a clean, verified solution. Work through every type before your exam.

How to solve this type
In base-N the only valid digits are 0 through N−1 — exactly N symbols. Spot an invalid digit by checking whether it is ≥ N: any digit with that value or higher cannot exist in that base. The classic trap is assuming base-10 digits (0–9) are always legal — they are not in, say, base-5 or base-7.

How many distinct digit symbols does a base-5 number system use?

A4B5C6D10

Which of the following is a valid single digit in a base-7 system?

A7B8C5D9