Binary Numbers Introduction

An introduction to Binary numbers with quiz questions along the way to check your knowledge.

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Binary Numbers Introduction

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An introduction to Binary numbers with quiz questions along the way to check your knowledge.
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Tags: Binary
  1. Binary Numbers

    Slide 1 - Binary Numbers

  2. It’s all about 1s and 0s

    Slide 2 - It’s all about 1s and 0s

    • Decimal numbers use 10 digits
    • 0,1,2,3,4,5,6,7,8,9
    • Binary numbers use 2 digits
    • 0,1
    • The basics are the same
  3. Decimal Numbers

    Slide 3 - Decimal Numbers

    • Each digit represents some number multiplied by a value for its location
    • 12 = one tens digit + two ones digits
    • 450 = four hundreds digits + five tens digits + zero ones digits
    • Each digit to the left represents ten times the digit to its right so ones, tens, hundreds, thousands, ten thousands, and so on
  4. Decimal or Base Ten

    Slide 4 - Decimal or Base Ten

    • The location value of each digit is any base where X represents the base is:
    • X4 + X3 + X2+ X1 + X0
    • Each digit has a value determined by how many values associated with that location it represents. Decimal numbers use powers of ten.
    • A 2 in the second location from the right is two times ten to the first power or two times ten to the first power. We call that twenty.
    • A 2 in the third location from the right is two times ten to the second power or two times one hundred. We call that two hundred.
  5. Decimal In Pictures

    Slide 5 - Decimal In Pictures

    • 1000
    • 100
    • 10
    • 1
    • 103
    • 102
    • 101
    • 100
    • 5
    • 2
    • 7
    • 9
    • 5
    • x
    • 1000
    • =
    • 5000
    • 2
    • x
    • 100
    • =
    • 200
    • 7
    • x
    • 10
    • =
    • 70
    • 9
    • x
    • 1
    • =
    • 9
    • 5279
  6. Binary Digits are powers of two

    Slide 6 - Binary Digits are powers of two

    • Each digit represents either one or zero times the location value for its position which is a power of 2
    • 1010 =
    • 1 x 23 + 0 x 22 + 1 x 21 + 0 x 20
    • 1 x 8 + 0 x 4 + 1 x 2 + 0 x 1
    • 8 + 0 + 2 + 0 = 10
    • 1111 =
    • 1 x 23 + 1 x 22 + 1 x 21 + 1x 20
    • 1 x 8 + 1 x 4 + 1 x 2 + 1 x 1
    • 8 + 4 + 2 + 1 = 15
  7. Binary in Pictures

    Slide 7 - Binary in Pictures

    • 8
    • 4
    • 2
    • 1
    • 23
    • 22
    • 21
    • 20
    • 1
    • 1
    • 1
    • 1
    • 1
    • x
    • 8
    • =
    • 8
    • 1
    • x
    • 4
    • =
    • 4
    • 1
    • x
    • 2
    • =
    • 2
    • 1
    • x
    • 1
    • =
    • 1
    • 15
  8. How do I know what Base?

    Slide 8 - How do I know what Base?

    • Subscripts are used to indicate number bases and remove ambiguity
    • 102 = 210
    • 110012 = 318 = 2510 = 1916
  9. Converting From Decimal to Binary

    Slide 13 - Converting From Decimal to Binary

    • Divide the number by 2 and record the remainder (0 or 1)
    • Divide the result by 2 and record the remainder to the left of the previous remainder
    • Continue until division results in zero
  10. For Example

    Slide 14 - For Example

    • Start with 1010
    • 10/2 = 5 with no remainder 0
    • 5/2 = 2 with a remainder of 1
    • 2/2 = 1 with a remainder of 0
    • 1/2 = 0 with a remainder of 1
    • Reading from bottom to top yields 10102
  11. Try Another

    Slide 15 - Try Another

    • Start with 1310
    • 13 / 2 = 6 with a remainder of 1
    • 6 / 2 = 3 with a remainder of 0
    • 3 / 2 = 1 with a remainder of 1
    • 1 / 2 = 0 with a reminder of 1
    • Reading from bottom to top yields 11012
  12. All Number Bases Work The Same

    Slide 20 - All Number Bases Work The Same

    • Base 8 (Octal) each digit is eight times the previous digit
    • Base 16 (Hexadecimal) each digit is sixteen times the previous digit
    • Mathematically this is expressed using exponents or “powers of” for the value of location of each digit
  13. Which sort of person are you?

    Slide 21 - Which sort of person are you?

    • There are 10 types of people in the world, those who understand binary and those who don’t.