Binary Number System Explained - IGCSE Computer Science (Convert & Add Binary)

Every photo, song, and message on a computer is stored as just two symbols: 0 and 1. This is the binary number system, and it's one of the most exam-tested topics in IGCSE Computer Science. In this lesson you'll learn why computers use binary, how to convert between denary and binary both ways, how to add binary numbers, and how to spot an overflow error — the exact skills examiners reward.

Why computers use binary

Computers are electronic. Every component is either on or off — there is no in-between state. Two states are easy to build reliably and hard to confuse, so we map "on" to 1 and "off" to 0. That single physical fact is why everything inside a computer is binary.

Bits, nibbles and bytes

A single binary digit is a bit. Four bits make a nibble. Eight bits make a byte — the standard unit you'll use throughout this topic.

Place values in an 8-bit byte

In an 8-bit byte each column has a fixed value, doubling from right to left. Memorise this row:

128   64   32   16   8   4   2   1

Converting denary to binary (division-by-2 method)

Keep dividing the number by 2, writing the remainder each time, until you reach zero. Then read the remainders from the bottom up. Example — convert 156: the remainders read bottom-to-top give 10011100. Check: 128 + 16 + 8 + 4 = 156.

Converting binary to denary (place-value method)

Write the place values above each bit, then add only the columns that hold a 1. For 10011100: 128 + 16 + 8 + 4 = 156.

Binary addition

Four rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 (write 0, carry 1 to the next column). Example — add 45 (00101101) and 23 (00010111): working right to left and carrying gives 01000100, which is 68.

Overflow errors

An 8-bit register can only hold eight bits. Adding 255 (11111111) and 1 needs a ninth bit — it has nowhere to go, so the register wraps around to zero. That lost carry is an overflow error.

Common exam mistakes to avoid

Forgetting to carry, reversing bit order, not padding your answer to 8 bits, and misaligning place values. Slow down and line the columns up.

Recap

Everything connects back to one idea — binary. From on/off states, through bits/nibbles/bytes and place values, to conversion, addition, and overflow.

Watch the full lesson: youtube.com/watch?v=1NFgrCYZzMk
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