How a Computer Counts
Bits and binary numbers
Read a binary number using the place values 1, 2, 4 and 8, and write a small ordinary number in binary.
A computer has no fingers to count on. Everything inside it is a switch that is either off or on, and we write those two states as 0 and 1. A single one of them is called a bit. Counting with only two digits is called binary, and it works exactly like ordinary counting — it just runs out of digits much sooner and has to start a new column.
The places
In an ordinary number the columns are 1, 10, 100, 1000 — each one ten times the last. In binary the columns are 1, 2, 4, 8, 16 — each one twice the last. To read a binary number, add up the place values that have a 1 in them and ignore the rest.
Have a play
Move along the line and count in ones. Every time you pass 1, 2, 4, 8 or 16 you are passing a place value that binary uses as a column.
Tap anywhere on the line.
Worked example
What does the binary number 1101 mean?
Write the place values above it, starting from the right: 8, 4, 2, 1.
The rightmost digit is always the ones. Every column to its left is worth double the one before.
Try it together
Now let us go the other way and write 10 in binary.
Start with the largest place value that will fit, and keep taking places until nothing is left over.
1.What is the largest binary place value that fits inside 10 — is it 4, 8 or 16?
Have a go
Have a go on your own. What is the binary number "1001" as an ordinary number?
Hint: Only two columns hold a 1, and they are the ones furthest apart.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.