Binary Numbers Introduction
Created 2 years ago
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An introduction to Binary numbers with quiz questions along the way to check your knowledge.

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Binary

Slide 1  Binary Numbers

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

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

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.

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

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

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

Slide 8  How do I know what Base?
 Subscripts are used to indicate number bases and remove ambiguity
 102 = 210
 110012 = 318 = 2510 = 1916

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

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

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

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

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.