JOHNNA NOLESECOMP7100

Binary Number System

What do computers do?

PC

Software

applications

images

textvideo

music

storage

Having a good unders tanding o f how b inary works i s fundamenta l to knowing many

o ther aspects o f how a l l d ig i ta l technology works , inc luding computers , networks ,

PDAs , ce l l te lephones , TVs , e tc .

Rationale

Ob j e c t i v e : t o r e a l i z e t h e i m p o r t a n c e o f t h e b i n a r y n u m b e r s y s t e m a n d c on v e r t n u m b e r s b e t w e e n b a s e - t e n a n d b a s e - t w o n u m b e r

s y s t e m s .

Processing Information

Electricity is either on or off.

1=on0=off

Decimal Numbers

Base-Ten System

01234567891011121314959697989910010115161718192021222324

103 102 101 100 10-1 10-2

Ones

Decimal Point

TensHundreds

Thousands

Expanded Form

103 102 101 100 10-1 10-2

OnesTens

Hundreds

Thousands

2 5 3

82000+500+30+8=2538

6 9 4

76000+900+40+7=6947

Binary Numbers

Base-Two System

0110111001011111000100110101011110011011110111110000110Dec

. Binary Number

0 0 0 0 0

1 0 0 0 1

2 0 0 1 0

3 0 0 1 1

4 0 1 0 0

5 0 1 1 1

24 23 22 21 20

16 8 4 2 1 Value

OnesTwos

Fours

Eights

Sixteens

Binary Numbers, Simplified

“Binary Numbers in 60 Seconds”YouTube

Converting: Binary to Decimal

24 23 22 21 20

16 8 4 2 1

1 0 0 1 0

(16x1)+ (8x0)+ (4x0)+ (2x1)+(1x0) =

1 1 0 1 0

(16x1)+ (8x1) + (4x0)+

(2x1)+(1x0) =

18

25

Converting: Decimal to Binary

24 23 22 21 20

16 8 4 2 1

11 =

28 =

0 1 0 1 1

1 1 1 0 0

Binary Addition

17 + 24 = ____

Excel Link

Partner Work

Assignment: With a partner, you have 5 minutes to convert decimal numbers to binary numbers.

Dec. Binary Number

14

9

21

10

25

1 1 1 0

1 0 0 1

0 1 0 1

1 0 1 0

1 0 0 1

0

0

1

0

1

Bits and Bytes Name Size

Bit 1, 0

Byte 8 bits

Kilobyte 2^10 = 1,024

Megabyte 2^20 = 1,048,576

Gigabyte 2^30 = 1,073,741,824

Terabyte 2^40 = 1,099,511,627,776

Petabyte 2^50 = 1,125,899,906,842,624

Exabyte 2^60 = 1,152,921,504,606,846,976

Zettabyte 2^70 = 1,180,591,620,717,411,303,424

Yottabyte 2^80 = 1,208,925,819,614,629,174,706,176

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