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Binary Numbers

Binary Numbers. So what are they and why are they important?. 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). Binary in Computing.

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Binary Numbers

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  1. Binary Numbers So what are they and why are they important?

  2. 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)

  3. 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”

  4. Understanding Binary • In the decimal system, let’s take the number: 150 for example: the “ones” column is represented by 0 The “tens” column is represented by 5 The “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.

  5. 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.

  6. 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.

  7. 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

  8. Binary System Lesson Plan

  9. 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.

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