Counting in Binary

Exploring Computer Science – Lesson 2-5

Let’s Play A Game

• Click to add text

Journal Entry

• How high can you count using 10 fingers?

Count the Dots• Let’s look at how binary numbers work…• Look at these cards:

• Count the dots on each card• Is there a pattern? What number comes next?• Can you define the numbers as powers of 2?

16 8 4 2 124 23 22 21 20

Numbers In Binary

• If I want to show the number 9 in binary– I need an 8– and 1

• In binary that’s 1001!

0 0 0 0 0 0 1 0 0 1

Numbers In Binary

• If I want to show the number 6 in binary– I need an 4– and 2

• In binary that’s 110!

0 0 0 0 0 0 0 1 1 0

Numbers In Binary

• If I want to show the number 19 in binary– I need an 16– and 2– and 1

• In binary that’s 10011!

0 0 0 0 0 1 0 0 1 1

Your Turn…

• In your journal write:The binary number for these decimal numbers:

2 =

14 =

31 =

The decimal number for these binary numbers:

1111 =

1010=

101=

Journal Entry

• Download “Lesson 2-5 - Secret Message” from the website.

• In your journals, decode the secret message

What does this have to with computers???

• Computers today use the binary system to represent information.

• It is called binary because only two different digits are used. It is also known as base two (humans normally use base 10).

• Each zero or one is called a bit (binary digit). A bit is usually represented in a computer’s main memory by a transistor that is switched on or off, or a capacitor that is charged or discharged.

What does this have to with computers???

• When data must be transmitted over a telephone line or radio link, high and low-pitched tones are used for the ones and zeros.

• On magnetic disks (floppy disks and hard disks) and tapes, bits are represented by the direction of a magnetic field on a coated surface, either North-South or South-North.

What does this have to with computers???

• Audio CDs, CD-ROMs and DVDs store bits optically—the part of the surface corresponding to a bit either does or does not reflect light.

What does this have to with computers???

• One bit on its own can’t represent much, so they are grouped together in groups of eight, which can represent numbers from 0 to 255. A group of eight bits is called a byte.

• That’s were get the get the terms– Kilobyte (1,024 bytes * 8 = 8,192 bits)– Megabyte (1,048,576 bytes * 8 = 8,388,608 bits)– Gigabyte (1,073,741,824 bytes * 8 =

8,589,934,592 bits) – That’s a lot of bits!

What does this have to with computers???

• Ultimately bits and bytes are all that a computer uses to store and transmit numbers, text, and all other information.

Try this out..

• For the next 10 minutes play this game

http://forums.cisco.com/CertCom/game/binary_game_page.htm

Journal Entry

• Imagine your fingers are “bits”. A finger that’s up is a “1” and a finger that is down is a “0”.

• In your journals calculate how high you can count using the fingers on 1 hand and then using the fingers on both hands.

Rest of TodayIndividual Assignment

• Download “Lesson 2-5 - More on Binary Numbers - Homework” from the website.

• Complete both parts and turn it in.– Make sure you answer all the questions in

each part fully and completely. Use complete sentences!

• Turn this today.

For Question 2 – Limit it to just these keys…