Numbers and Data
Bigger binary numbers
Read and write binary numbers with several places, and work out how many different values a given number of bits can hold.
Binary has only two digits, so it needs more places than ordinary numbers do. The rule for the places is the only thing to remember: the place on the far right is worth 1, and every place after it is worth twice the one to its right. That is why binary numbers look long — six binary places do the work that two ordinary digits do.
Reading and writing are two directions of the same trick
To read a binary number, add up the place values that have a 1 under them. To write one, hunt for the largest place value that still fits inside your number, put a 1 there, take it away, and hunt again in what is left. Every place you skip past gets a 0, and those zeros matter as much as the ones.
Worked example
Write the number 45 in binary.
Find the largest place value that fits inside 45. Doubling upwards from 1 reaches 32, and doubling once more overshoots 45, so 32 is the one to use.
Starting from the largest place is what stops you needing to go back and change a digit later.
Have a play
Move along this line and think about which binary places you would need to reach each point.
Tap anywhere on the line.
Try it together
Now read this one together: what is the binary number 11010 worth?
Work from the left-hand digit, keeping track of the place you are on.
1.There are five digits, so the left-hand one sits in which place? Write the place value as a number.
Have a go
Have a go on your own. Write the number 25 in binary.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.