Binary Numbers
description
Transcript of Binary Numbers
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Binary Numbers
So what are they and why are they important?
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Decimal System vs. Binary System
• The Decimal System is a Base 10 system. That simply means it uses 10 symbols.
(0,1,2,3,4,5,6,7,8,9)
• The Binary System is a Base 2 system. It only uses 2 symbols. (0 and 1)
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Binary in Computing Necessary for only 2 symbols because computers/ electronics
recognize only: “ON” (represented by 1) or “OFF” (represented by 0)
For computers, this 2 symbol system is crucial because it increases speed, memory and utilization
These binary digits (“0” and “1”) are known as “bits”
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Understanding Binary
• In the decimal system, let’s take the number: 150 for example:
the “ones” column is represented by 0The “tens” column is represented by 5The “hundredths” column is represented by 1
As we go from right to left, the columns represent increasing powers of 10. Ones to tens, tens to hundredths, etc.
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Understanding Binary• However, the Binary Number System, from
right to left increases in powers of 2.• (128, 64, 32, 16, 8, 4, 2, 1)
• So, since we can easily figure out the value of each column: we can deduce what the number is judging by whether there is a “1” (yes to that value) or “0” (none of that value) in that column.
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Binary numbers
• Let’s take the binary number: 10
The column on the far right is the 1 column and the 0 indicates no value present.
The column on the left is the 2 column and the “1” means there is a value of 2 present.
So 10 in binary (remember this reads as 1 and 0, not
“ten”)= 2 in the decimal system.
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Binary Numbers• Now’s let’s watch a brief video to better
understand how to convert the numbers from binary to decimal and vice versa.
Binary Numbers in 60 seconds: http://www.youtube.com/watch?v=qdFmSlFojIw&NR=1
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Binary System Lesson Plan
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References“Binary Numbers” image retrieved from http://atgfw.com/data.html.
Video retrieved on 9/18/2011 from: http://www.youtube.com/watch?v=qdFmSlFojIw&NR=1.
Website retrieved on 9/18/11 from: http://www.kerryr.net/pioneers/binary.htm.
Website retrieved on 9/19 from: http://homepage.ntlworld.com/interactive/.
Website retrieved on 9/19 from: http://www.math.grin.edu/~rebelsky/Courses/152/97F/Readings/student-binary.
Website retrieved on 9/19 from: http://www.helpwithpcs.com/courses/binary-numbers.htm.
Website retrieved on 9/19 from: http://www.state.nj.us/education/cccs/standards/8/index.html.