Binary is a base 2 number system as it represents numbers with just 2 digits, either 0 or 1. We are more used to using a base 10 number system with 10 different digits (0,1,2,3,4,5,6,7,8,9).
To quickly recap what we already know, with the base ten system, we may have a number, say 6789, and within this number we know that the digit 9 represents units, the digit 8 represents tens, the digit 7 represents hundreds and the digit 6 represents thousands – and we spend considerable time teaching pupils such fundamental understanding of place value i.e. that it is the column in which the digit appears which determines the value it represents. This principle of place value is exactly the same in binary with the only difference being the value of the columns.
In binary we do not have each column value increasing in multiple of ten (units, tens, hundreds etc) rather they increase as follows:
128s 64s 32s 16s 8s 4s 2s 1s
Let me provide a binary number to illustrate this:
1 1 0 1
As mentioned, the binary number above is made up of only 2 digits: 0s and 1s. To read this number we need to reference back to what each of these 0s and 1s represents.
The 1 in the first column from the right represents 1s (So we have 1 lot of 1 which equals 1)
The 0 in the second column from the right represents 2s (So we have 0 lots of 2 which equals 0)
The 1 in the third column from the right represents 4s (So we have 1 lot of 4 which equals 4)
The 1 in the forth column from the right represents 8s (So we have 1 lot of 8 which equals 8)
So altogether we have 1 + 0 + 4 + 8 = 13. So this is the binary representation of the number 13.
Here is a table with the numbers 10 – 15 in binary to provide further examples of reading binary.
To check your understanding, can you write the numbers 17 and 18 in binary? (Answer: 10001, 10010)
How can Numicon be used to support the teaching of binary?
The following visual representations of the base 10 digits 1 through 9 make up part of the Numicon apparatus.
These could be used to support teaching the basics of reading and writing binary, as we have covered here, by providing pupils just the 1, 2, 4 and 8 shapes (since these are values of the first four digits of a binary number) and challenging pupils to find ways to create the numbers 0 – 15 with just these blocks
e.g. How can we make 7? 1 + 2 + 4. How can we make 11? 8 + 2 + 1.
Pupils could be asked to tabulate their work by recording in a table with a tick or cross whether they used each block. This may look something like this (shown here just for numbers 1 – 5):
From the table above by simply replacing the ticks and crosses with either a 1 or 0 the binary representation for each of the numbers can be arrived at, simple 🙂