Module 5.1 "Binary and Other Numbering Systems" Study Guide

Lesson 5.1 “Binary and Other Numbering Systems” Objectives

• 1.2 Identify notational systems.

• 2.3 Compare and contrast storage types.

“Binary Basics” (5.1.1)

• Computers understand everything in binary, which is a system of counting using only two values: on or off, true or false, yes or no, 1 or 0. You can think of a light switch as a binary system, because it is always either on or off, just like binary.

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Bits

• The smallest unit of measure for a computer

• Each bit can store just one of two values: one or zero, present or absent. This numbering system is the foundation of modern computers.

• Early computers from the 1940s used vacuum tubes, which looked similar to light bulbs, to process information

• We measure Internet speeds and network data transfer rates in how fast they can move these tiny pieces of information.

• Bits, the smallest unit of measure, are always abbreviated with a lower-case or small letter b. When we talk about transfer rates, the K in kilo- and the M in megabit (and the G in gigabit, and so on), are all capitalized, but the bit is always lower-case.

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Bytes

• The only thing a computer can understand is encoded in bits

• The most common group of bits is called a byte.

• A byte is made up of eight bits.

• A single byte, in this simplest form, can store one of 256 values.

• This is because there are 256 possible combinations that those eight 1s and 0s can create.

• Bytes are the basic unit of storage in computing, which is why we describe storage in kilobytes (KB), megabytes (MB), gigabytes (GB) and so on.

• Bytes are always abbreviated with an upper-case or capital letter B.

Binary As Storage (5.1.2)

Information Coding Formats

• Because the way a computer stores anything is in bits and bytes, humans have to translate everything that we can read into binary before we can store it

• most commonly used ways to encode this information is in the ASCII format.

• The American Standard Code for Information Interchange (ASCII) format includes lower-case letters, upper-case letters, the numbers 0 through 9, and common symbols such as ( and ), #, ^, and quotation marks.

• This system uses bytes to represent the characters you see on a computer screen.

• The ASCII format got started before computers became common, and because of this it only has 128 characters in its code.

• characters were all based on the English language and didn't include characters from other widely known languages

• The Unicode Consortium, a non-profit group, developed the Unicode Standard to improve on the ASCII format. The Unicode Standard provides a unique number for every character, no matter what platform, device, application or language. Unicode even supports emojis.

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Storing in Binary

• As you add more and more bytes, they build into useful measures of storage capacity. If you have 1024 bytes, this is equal to 1 kilobyte (KB).

• As you add kilobytes up to 1024KB, you have a megabyte (MB). If you add on more megabytes, then at 1024 megabytes you have a gigabyte (GB), and so on.

• Measuring capacity in this way, with large numbers of bytes, applies to system memory and to data storage in solid state and hard disk drives. Remember that most kinds of memory are non-persistent or volatile storage, and only holds those bytes of data as long as the computer is powered on.

Hexadecimal And Octal Systems (5.1.3)

• One of the main drawbacks of binary, from a human perspective, is how difficult it is to understand. The hexadecimal numbering system is one way to bridge this gap.

• Hexadecimal (also called simply 'hex') is a base-16 numbering system. Each digit represents sixteen numbers (from zero to fifteen). In hexadecimal, the familiar numbers 0 - 9 represent those same numbers, and the letters A - F represent 10 through 15.

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Hexadecimal in Computing

• very useful in computer programming and networking.

• Hex numbers are compact and use less memory, so more numbers can be stored in computer systems. It is also useful to represent computer memory addresses.

• Developers use it to describe colors on webpages, describe memory locations for each byte, to specify certain characters and more.

• In IT environments, you will see many hexadecimal numbers representing various aspects of computer networks.

• The hexadecimal system is used, in part, because it translates well to binary. Their simplified form in representing binary values is compact and easier to read.

• Because binary numbers can get very large, using a hex number takes fewer digits (and therefore, less storage).

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Hexadecimal in Network Addresses

• Each hexadecimal digit represents four bits

• Hexadecimal numbers are used with some newer types of internet protocol (IP) addresses

• You will also see this numbering system used with media access control (MAC) addresses

• Every device that can connect to a network, from your smartphone to the office copier, will have a unique MAC address.

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Octal Numbering

• The octal system is a base-8 numbering system that uses the digits 0 - 7. Just like hexadecimal, octal can represent binary numbers in much smaller spaces.

• While most of the IT world does not use octal very frequently, it's important to know that this system is used in low-level programming and coding, including some assembly languages.

• In addition, Linux and UNIX operating systems use octal numbers to represent file permissions.

• Each digit in the octal number indicates a set of three permissions (either read, write, or execute) for different accounts.