1. CISCO NETWORKING ACADEMY Chabot College ELEC 99.05 Binary Introduction

2. CISCO NETWORKING ACADEMY Binary and Computing To make it easier to work with a computer’s states of “on” and “off,” we use a numbering system that only has two possible values. This numbering system is called “base 2,” or “binary.”

3. CISCO NETWORKING ACADEMY Binary Numbering System In the binary numbering system, each digit has two possible values: 0 or 1

4. CISCO NETWORKING ACADEMY One Bit Therefore, with 1 digit or “bit”, we can have two possible combinations: 1 bit: 2 1 = 2 values 0 1

5. CISCO NETWORKING ACADEMY Two Bits With 2 digits or “bits”, we can have four possible combinations: 2 bits: 2 2 = 4 values 0 1 0 0 01 11

6. CISCO NETWORKING ACADEMY Three Bits 3 bits: 2 3 = 8 possible values : 0 1 0 0 01 1 1 0 0 0 01 1 1 1 00 01 10 11

7. CISCO NETWORKING ACADEMY 1 - 8 Bits 1 bit: 2 1 = 2 possible values 2 bits: 2 2 = 4 possible values 3 bits: 2 3 = 8 possible values 4 bits: 2 4 = 16 possible values 5 bits: 2 5 = ? 6 bits: 2 6 = ? 7 bits: 2 7 = ? 8 bits: 2 8 = ?

8. CISCO NETWORKING ACADEMY Binary Numbering System Each value is a binary digit, or bit for short. 01111000 Eight bits together make a unit called a byte. In IP addresses, bytes are called octets (group of eight).

9. CISCO NETWORKING ACADEMY Not exactly… Eight bits together make a unit called a byte, BUT… Seven bits grouped together are also, sometimes, referred to as a byte. Example: 7-bit ASCII characters. “Octet” is used to be unambiguous.

10. CISCO NETWORKING ACADEMY Special Binary Values BitsValuesUse/Signpost 42 4 = 16Hex numbers (0 - F) 72 7 = 128ASCII characters 8 (byte)2 8 = 256“octet”, extended ASCII 102 10 = 1,024“K”, “kilo” thousand 16 (2 bytes)2 16 = 65,536 64“K” 202 20 = 1,024K “meg” (2 10 x 2 10 ) million 24 (3 bytes)2 24 = 16,384K“16 megs”(2 4 x 2 10 x 2 10 ) 30 2 30 “gig”(2 10 x 2 10 x 2 10 ) billion

11. CISCO NETWORKING ACADEMY Binary Numbering System In decimal, each place value is a power of ten. We read the number 2342 as two-thousand three-hundred forty-two. 1101001000 2432 10 0 10 1 10 2 10 3

12. CISCO NETWORKING ACADEMY Binary Numbering System In binary, each place value is a power of two. The byte 11001111 is equivalent to 207 in decimal. 124 111 81632 100 64128 11 2020 21212 2323 2424 2525 2626 2727

13. CISCO NETWORKING ACADEMY Practice Slide 124 ??? 81632 ??? 64128 ?? 2020 21212 2323 2424 2525 2626 2727

14. CISCO NETWORKING ACADEMY Binary Blitz Contest Gameplay: You are blue and the computer is red. Click START. A random target number from 1 to 255 will be displayed at the right. Use the mouse to toggle the blue zeros and ones until they are the binary equivalent of the decimal number target. Show your screen to the instructor for bonus credit when your score = 10. Double credit for score > 20. Get Binary Blitz free at http://ganns.com