Computer Science123Updated 14 Oct 20262 pages

Understanding Binary and Denary Place Values - GCSE Notes

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Ever wondered how computers actually understand information? It all comes down to binary - a simple system using just 1s and 0s that powers everything digital around you. Let's decode how this works and why it's absolutely crucial for computing.
Binary and Denary with Place Values Notes – page 1

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Understanding Binary Basics

Think of binary as the computer's native language - it only speaks in 1s and 0s! Each binary digit (bit) is like a tiny switch that's either on (1) or off (0). This might seem limited, but these simple combinations can represent absolutely anything - your favourite song, photos, text messages, or complex games.

In daily life, you're used to denary (also called decimal or base 10), which uses digits 0-9. The number base tells you how many different digits are available in that system. Since denary has 10 digits 0−90-9, it's base 10. Binary is base 2 because it only uses two digits: 0 and 1.

Here's the brilliant bit - every denary number you know has a perfect binary equivalent! Understanding denary place values is your first step. Take 6432: it breaks down into thousands, hundreds, tens, and ones. Each column represents a power of 10 - thousands (10³), hundreds (10²), tens (10¹), and ones (10⁰).

Quick Tip: Remember that any number to the power of 0 equals 1 - that's why the ones column is 10⁰!

Binary and Denary with Place Values Notes – page 2

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Converting Binary to Denary

Binary place values work exactly like denary, except each column represents a power of 2 instead of 10. This is where the magic happens! Let's crack the code with binary number 1001.

Set up your columns: eights (2³), fours (2²), twos (2¹), and ones (2⁰). Place your binary digits underneath: 1001 becomes 1 in eights, 0 in fours, 0 in twos, and 1 in ones.

Now for the conversion: multiply each digit by its place value, then add them up. So (1×8) + (0×4) + (0×2) + (1×1) = 8 + 0 + 0 + 1 = 9. The binary number 1001 equals 9 in denary!

Memory Hack: The place values in binary double each time: 1, 2, 4, 8, 16, 32... Learn this sequence and you'll convert like a pro!

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