Binary

# Binary Numbers Introduction

Created 3 years ago

Duration 0:07:57
288
An introduction to Binary numbers with quiz questions along the way to check your knowledge.
Slide Content
Tags: Binary

2. ### 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. ### 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. ### 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.

• 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. ### 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

• 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. ### 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. ### 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. ### Slide 14 - For Example

• 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