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Johnna Noles Ecomp7100 Binary Number System
What do computers do?
Having a good understanding of how binary works is fundamental to knowing many other aspects of how all digital technology works, including computers, networks, PDAs, cell telephones, TVs, etc. Rationale Objective: to realize the importance of the binary number system and convert numbers between base-ten and base-two number systems.
Processing Information Electricity is either on or off. 1=on 0=off
Decimal Numbers Base-Ten System 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 95 96 97 98 99 100 101 15 16 17 18 19 20 21 22 23 24 Thousands Hundreds Tens Ones 103 102 101 100 10-1 10-2 Decimal Point
Expanded Form Thousands Hundreds Tens Ones 103 102 101 100 10-1 10-2 2 5 3 8 6 9 4 7 2000+500+30+8=2538 6000+900+40+7=6947
Binary Numbers Base-Two System 0 1 10 11 100 101 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 110 Sixteens Eights Fours Twos Ones 24 23 22 21 20 16 8 4 2 1 Value
Binary Numbers, Simplified “Binary Numbers in 60 Seconds” YouTube
Converting: Binary to Decimal 24 23 22 21 20 4 2 1 8 16 1 0 0 0 1 (16x1)+(8x0)+(4x0)+(2x1)+(1x0) =  18 1 0 1 0 1 (16x1)+(8x1)+(4x0)+(2x1)+(1x0) =  25
Converting: Decimal to Binary 24 23 22 21 20 4 2 1 8 16  11 =  1 1 1 0 0  28 =  0 1 0 1 1
Binary Addition Excel Link   17 + 24 = ____
Partner Work Assignment: With a partner, you have 5 minutes to convert decimal numbers to binary numbers. 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1
Bits and Bytes
Easy Conversions
Summary Bits are binary digits.  Each bit can hold the value 0 or 1. Bytes are made up of 8 bits each.  Binary math works just like decimal math, but each bit can have a value of only 0 or 1.  Microchips use transistors to process the information (on and off electrical currents) so the computer understands it.
“There are only 10 kinds of people in this world, those who understand binary and those who don’t.”
References MathCrazyTutoring. (2007, February 13). Binary code in 60 seconds [Video file]. Retrieved from http://www.youtube.com/watch?v=qdFmSlFojIw Binary primer. (n.d.). Retrieved from http://www.lesley.edu/faculty/wbarowy/c7100H/Binary.html Brian, M. (2000, April 1). How Bits and Bytes Work. Retrieved from http://computer.howstuffworks.com/bytes.htm

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Binary Slides

  • 1. Johnna Noles Ecomp7100 Binary Number System
  • 3. Having a good understanding of how binary works is fundamental to knowing many other aspects of how all digital technology works, including computers, networks, PDAs, cell telephones, TVs, etc. Rationale Objective: to realize the importance of the binary number system and convert numbers between base-ten and base-two number systems.
  • 4. Processing Information Electricity is either on or off. 1=on 0=off
  • 5. Decimal Numbers Base-Ten System 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 95 96 97 98 99 100 101 15 16 17 18 19 20 21 22 23 24 Thousands Hundreds Tens Ones 103 102 101 100 10-1 10-2 Decimal Point
  • 6. Expanded Form Thousands Hundreds Tens Ones 103 102 101 100 10-1 10-2 2 5 3 8 6 9 4 7 2000+500+30+8=2538 6000+900+40+7=6947
  • 7. Binary Numbers Base-Two System 0 1 10 11 100 101 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 110 Sixteens Eights Fours Twos Ones 24 23 22 21 20 16 8 4 2 1 Value
  • 8. Binary Numbers, Simplified “Binary Numbers in 60 Seconds” YouTube
  • 9. Converting: Binary to Decimal 24 23 22 21 20 4 2 1 8 16 1 0 0 0 1 (16x1)+(8x0)+(4x0)+(2x1)+(1x0) = 18 1 0 1 0 1 (16x1)+(8x1)+(4x0)+(2x1)+(1x0) = 25
  • 10. Converting: Decimal to Binary 24 23 22 21 20 4 2 1 8 16 11 = 1 1 1 0 0 28 = 0 1 0 1 1
  • 11. Binary Addition Excel Link 17 + 24 = ____
  • 12. Partner Work Assignment: With a partner, you have 5 minutes to convert decimal numbers to binary numbers. 1 1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 1
  • 15. Summary Bits are binary digits. Each bit can hold the value 0 or 1. Bytes are made up of 8 bits each. Binary math works just like decimal math, but each bit can have a value of only 0 or 1. Microchips use transistors to process the information (on and off electrical currents) so the computer understands it.
  • 16. “There are only 10 kinds of people in this world, those who understand binary and those who don’t.”
  • 17. References MathCrazyTutoring. (2007, February 13). Binary code in 60 seconds [Video file]. Retrieved from http://www.youtube.com/watch?v=qdFmSlFojIw Binary primer. (n.d.). Retrieved from http://www.lesley.edu/faculty/wbarowy/c7100H/Binary.html Brian, M. (2000, April 1). How Bits and Bytes Work. Retrieved from http://computer.howstuffworks.com/bytes.htm

Editor's Notes

  1. 5
  2. 2
  3. 2 “Computers process information by the way they use electricity.  The number one is represented by the electricity being switched on and zero is represented by the electricity being switched off (A Binary Primer).” 
  4. 2 Explain the decimal numbers we use today (ones, tens, hundreds, thousands, etc.). Show the relation between place value and powers of 10.
  5. 3 5. Expanded form examples: Show the number 2,538. Briefly explain the place value of each digit. Point to different digits in the number 6,947 and ask students to name the value of the digit. Show the way that we carry place value from ones to tens when adding.
  6. 3 “Computers process complex information by encoding it in a system of ones and zeros, called binary. The binary number system uses only ones and zeros (Binary Primer).” Explain the base-two place values, or powers of two. “Each cell contains a binary digit (bits).” Show table from library and ask what patterns are noticed (odd numbers, even numbers, twos place, fours place, etc.).
  7. 1
  8. 4 Demonstrate converting 010010 and 0011010from binary to decimal.
  9. 3 Demonstrate converting 11 and 28 from decimal to binary.
  10. 7 Practice: Introduce Excel sheet. Ask students how to convert 17 and 24. Show sum and explain how base-two systems carry to the next place.
  11. 6 Using the binary handout, have students work with a partner for 5 minutes to convert between decimal and binary numbers. Quickly review answers, allowing students time to correct mistakes as needed.
  12. 3Binary Multipliers: Review chart and relate to internal and external memory.
  13. 5 Windows Calculator: Demonstrate how to use the Windows Calculator to convert numbers between binary and decimal.
  14. 1“In conclusion, bits are binary digits. Each bit can hold the value 0 or 1. Bytes are made up of 8 bits each. Binary math works just like decimal math, but each bit can have a value of only 0 or 1. Microchips use transistors to process the information (on and off electrical currents) so the computer understands it.”
  15. 2