In this lesson we will start to learn about Binary numbers. We need to understand this really well if we want to be able to use our computers or microprocessors to process data from sensors and to send signals to actuators or other output devices.
Binary numbers use a very simple Alphabet containing only two symbols: 0 and 1
Please watch the following 10 minute video from Khan Academy (for a larger video image, click either on the Full Screen icon in the lower right corner, or the YouTube logo to the left of it)
I see that many people are confused by the conversion of 231 Decimal to 11100111 Binary. The common questions are where did the zeroes come from, or how did he know which were 1 and which were 0.
This will be covered in a few lessons time.
There was also the use of exponents (the small numbers that are raised up) like 102 , 101 , 100,
and the same for the binary numbers with column values from 27 down to 20.
This will also be covered in a few lessons time.
Lastly, there were questions about why, when showing the values for the eight binary digit positions with the exponent style (like 27), where did the 2 come from since Binary only has 0 and 1 . In explaining the values of each of the digit positions for Binary numbers, the video used the familiar Decimal numbers. So the 2 and the 7 are part of the Decimal alphabet being used to explain the Binary digit position values. Since both Decimal and Binary are just number systems that that use different alphabets, it should be possible to explain the Binary number system digit positions using the Binary alphabet. If we only use Binary number with 3 digits, there are eight possible numbers:
So instead of writing 27 (using the Decimal alphabet) we could instead write 010111 using only the Binary Alphabet (symbol set).
We will explore this more in a future lesson.