CISCO NETWORKING ACADEMY Chabot College ELEC Binary Introduction

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.”

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

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

CISCO NETWORKING ACADEMY Two Bits With 2 digits or “bits”, we can have four possible combinations: 2 bits: 2 2 = 4 values

CISCO NETWORKING ACADEMY Three Bits 3 bits: 2 3 = 8 possible values :

CISCO NETWORKING ACADEMY 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 = ?

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

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.

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 = 1,024“K”, “kilo” thousand 16 (2 bytes)2 16 = 65,536 64“K” = 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 ) “gig”(2 10 x 2 10 x 2 10 ) billion

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

CISCO NETWORKING ACADEMY Binary Numbering System In binary, each place value is a power of two. The byte is equivalent to 207 in decimal

CISCO NETWORKING ACADEMY Practice Slide 124 ??? ??? ??

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