Binary numbers are based on the concept of ones and zeros or something similar to on and off.

The base used to count in binary number is 2 and the one and zero says whether that 2 is on or off. The position of the one or zero in the binary number tells you to what power to raise the \(2 .\)

You can think of binary as adding all the powers of 2 from left to right, where 1 means add the power and 0 means dont add the power.

\(16,8,4,2,1\) are the powers of 2 in reverse order. If we wanted to write the number 12 , we can see that we would need to add (switch on) the 4 and the 8 , all the other positions are off. So to write 12 as a binary number we would say 1100 .

Here is another example -

write 25 as a binary number (always start with the biggest numbers first) so \(16+9\) gives us 25 , so we switch on the 16 , now we look for what will give us \(9.8+1\) gives us 9 so we switch on the 8 and the 1. Now we can write 25 in binary as \(11001 .\)

This process can also be reversed in order to translate a binary number into a decimal number. For example, write 101011 as a decimal number. This means that we have \(1 \times 2\) to the power of \(5(\) position \(6-1)+0 \times 2\) to the power of \(4+1 \times 2\) to the power of \(3+0 \times 2\) to the power of \(2+1 \times\) to the power of \(1+1 \times 2\) to the power of 0 . This gives us \(32+0(16)+8+0(4)+2+1=43\).

This is the long way of converting between binary and decimal numbers. We can also convert these numbers on our SHARP scientific calculators (this will work the same way on the ELW531, EL-W535 and the EL-W506). Type 43 into your calculator then press 2 nd \(F\) and the divide button (above it in an orange block you should see an arrow and the word BIN), this will convert 43 into binary - \(101011 .\)

Now type in a binary number, for example 11100111 and then press 2 nd \(\mathrm{F}\) and the + button (above it in an orange box you should see an arrow and the word DEC). This will convert the binary number back into a decimal number - in this case, \(231 .\)