Binary numbers: counting with two symbols — Computing, 7–10
Computers use patterns of 0 and 1 to represent numbers. Learning the pattern shows how switches can build larger amounts.
Idea
Our usual number system has ten digits, but binary has only two: 0 and 1. Each place is worth twice as much as the place to its right: 1, 2, 4, 8 and so on. A 1 means “use this value” and a 0 means “leave it out”, like switches in a row.
Why it exists
Tiny electronic parts can reliably be in one of two states: a signal is present or it is not. Using 0 and 1 matches those two states, so the machine does not need to guess about a halfway signal. Groups of these simple choices can still represent numbers, letters, colours and sounds.
Worked example
Let’s write 13 in binary using place values 8, 4, 2 and 1. Step 1: 13 includes 8, so write 1 and have 5 left. Step 2: it includes 4, so write 1 and have 1 left. Step 3: it includes no 2, so write 0. Step 4: it includes 1, so write 1. The answer is 1101, because 8 + 4 + 0 + 1 = 13.
A common trap
It is easy to read 101 as “one hundred and one”, because that is what the same marks mean in our usual system. In binary, the places are 4, 2 and 1, so 101 means 4 + 0 + 1 = 5. The marks are not enough by themselves; their place values tell you what they mean.
Outside school
Binary patterns are used inside phones, cameras, game consoles and smart appliances. You usually see the final photo or sound, not the 0s and 1s underneath. Understanding binary helps you see that digital things are built from many tiny, reliable choices rather than from mysterious magic.
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