Information Support and Services 2.01 Understand how computers and high tech communication devices work.

Number Systems and Codes Translate number systems and codes Representations Systems Groupings Translations Codes

Translate number systems and codes Why study number systems and codes? Computers and smart devices are all based on circuits that work with only two states; on and off. These states are represented by the binary numbers 0 and 1. All data must be converted to binary code before being processed.

Translate number systems and codes Representations Data can be represented in two forms: Analog Digital The majority of modern computers are digital devices.

Translate number systems and codes Representations Analog: Measuring or representing data by means of one or more physical properties that can express any value along a continuous scale.

Translate number systems and codes Representations Digital: Expressed in discrete numerical form, especially for use by a computer or other electronic device.

Translate number systems and codes This course focuses on three number systems: Decimal: The number system people use. Binary: The number system most computers use. Hexadecimal: A number system that is used to make binary numbers more compact.

Translate number systems and codes Decimal: Base 10 0,1,2,3,4,5,6,7,8,9

Translate number systems and codes Decimal: Place Weights 1 2 7 5 103 102 101 100 5x100 = 5 7x101 = 70 2x102 = 200 1x103 = 1,000 TOTAL 1,275 Any number raised to the power of zero is 1

Translate number systems and codes Binary: Base 2 1

Translate number systems and codes Why Binary? Computers are digital devices. They are made of millions of tiny transistors which are operated in one of two states – OFF (0) or ON (1)

Translate number systems and codes Binary: Place Weights 1 23 22 21 20 1x20 = 1 1x21 = 2 0x22 = 1x23 = 8 TOTAL 11 The only digits in a binary number are 0 & 1. This is the decimal equivalent

Translate number systems and codes Hexadecimal: Base 16 We only use 10 digits, so letters are added. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

Translate number systems and codes Why Hexadecimal? Large binary numbers are difficult for humans to work with; hexadecimal is a more compact form. It is quicker to convert between binary and hexadecimal than binary and decimal. These are all the same number: 1010 0100 1010 0011 A 4 A 3 42,147

Translate number systems and codes Hexadecimal: Place Weights 2 A C 163 162 161 160 Cx1 = 12 Ax16 = 160 2x256= 512 0x4096= TOTAL 684 This is the decimal equivalent

Translate number systems and codes Where are some places hexadecimal numbers are commonly used? The physical (MAC) address of a network card. Color codes in html.

Translate number systems and codes Binary Grouping Bit Nibble Byte BYTE (8 BITS) 1 Nibble (4 bits) (One hex digit) BIT

Translate number systems and codes SI (International System) Units The following metric prefixes are used to condense binary numbers: Kilobit kb Megabit Mb Gigabit Gb Terabit Tb Kilobyte kB Megabyte MB Gigabyte GB Terabyte TB Typical Internet Speed = 1.5 Mb/s (Megabits per second) Hard disk drive size= 1 TB (terabyte)

Translate number systems and codes Conversions It is often necessary to be able to perform the following conversions: Decimal to Binary Binary to Decimal Decimal to Hexadecimal Hexadecimal to Decimal Binary to Hexadecimal Hexadecimal to Binary

Translate number systems and codes Remember: A computer only operates on binary numbers! Codes American Standard Code for Information Interchange ASCII (pronounced as-key) A way of expressing text and other non-numerical characters in binary code. Character Hex Binary A 41 0100 0001 a 61 0110 0111

Translate number systems and codes ASCII Text documents must be stored as numbers on the computer’s hard drive. Text messages are transmitted as ones and zeros over the wireless network. 1010101 1010101

Translate number systems and codes Unicode The Unicode standard assigns codes to characters in many languages so a computer can recognize these characters. Sample codes: UTF-8 UTF-16 UTF-32 The number of characters represented increases as the UTF designation increases.

Translate number systems and codes Unicode The dominant scheme for internal processing and storage of text UTF-8 is the most common Unicode encoding for HTML documents on the World Wide Web. utf-8

Information Systems Websites http://openbookproject.net/electricCircuits/Digital/DIGI_1.html Open Book Project - Lessons In Electric Circuits -- Volume IV