Understand the denary, binary and hexadecimal number systems

📚 Data Representation: Denary, Binary & Hexadecimal

1️⃣ Denary (Decimal) – The Number System We Use Every Day

Denary, also called decimal, is the base‑10 system. It uses ten digits: 0,1,2,3,4,5,6,7,8,9. Each position represents a power of 10. For example:

$123_{10} = 1\times10^2 + 2\times10^1 + 3\times10^0$

Think of it like counting on your fingers – each finger adds a new “place” (10, 100, 1000, …).

2️⃣ Binary – The Language of Computers

Binary is base‑2, using only 0 and 1. Each position represents a power of 2. Example:

$10_{10} = 1010_2$

Analogy: binary is like a light switch – it can be either OFF (0) or ON (1). Computers use millions of such switches to store data.

Conversion steps (decimal to binary):

1. Divide the decimal number by 2.
2. Record the remainder (0 or 1).
3. Repeat with the quotient until it becomes 0.
4. The binary number is the remainders read in reverse order.

3️⃣ Hexadecimal – A Shorter Way to Write Binary

Hexadecimal is base‑16. It uses digits 0–9 and letters A–F (representing 10–15). Each hex digit equals four binary digits (bits). Example:

$255_{10} = FF_{16} = 11111111_2$

Analogy: Think of hex as a shorthand “word” for a long binary string – like writing “k” instead of “1000000” in binary.

Conversion steps (decimal to hex):

1. Divide the decimal number by 16.
2. Record the remainder (0–15). If 10–15, use A–F.
3. Repeat with the quotient until it becomes 0.
4. Read the remainders in reverse to get the hex value.

🗂️ Quick Reference Table (0–15)