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  • 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).” 
  • 2 Explain the decimal numbers we use today (ones, tens, hundreds, thousands, etc.). Show the relation between place value and powers of 10.
  • 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.
  • 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.).
  • 1
  • 4 Demonstrate converting 010010 and 0011010from binary to decimal.
  • 3 Demonstrate converting 11 and 28 from decimal to binary.
  • 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.
  • 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.
  • 3Binary Multipliers: Review chart and relate to internal and external memory.
  • 5 Windows Calculator: Demonstrate how to use the Windows Calculator to convert numbers between binary and decimal.
  • 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.”
  • 2

Binary Slides Binary Slides Presentation Transcript

  • 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