Understanding Binary Numbers

Introduction: Understanding Binary Numbers When working with Digital Media, it’s imperative that you posses a basic understanding of how computers save, transfer, and process data. In order to visualize and conceptualize you should first build and understanding of the binary number system.

Introduction: Understanding Binary Numbers 1 of 7 Elements Introduction Introduction: Understanding Binary Numbers If you have ever seen the movie “The Matrix” and enjoyed thinking about how it all works; jumping in and out of a computer program etc… Then you know something about conceptualizing. To form (a concept or concepts) out of observations, experience, data, etc. When you use your brain to visualize something that is abstract or on the surface a bit difficult to see in your mind.

Understanding Binary Numbers The binary number system, also called the base-2 number system, is a method of representing numbers by using combinations of only two numerals: zero (0) and one (1). Computers use the binary number system to manipulate and store all of their data including numbers, words, videos, graphics, and music.

Learning Objective: After this lesson students should be able to:   Briefly explain what binary numbers are. Briefly explain what decimal numbers are. Explain why we need to understand binary numbers. Count with binary numbers. Convert decimal numbers to binary. Convert binary numbers to decimal. Demonstrate an expanded vocabulary. Understand the history of Binary numbers.

In 1854, British mathematician George Boole published a landmark paper detailing an algebraic system of logic that would become known as Boolean algebra. His logical calculus was to become instrumental in the design of digital electronic circuitry.

History of Binary In November 1937, George Stibitz, then working at Bell Labs, completed a relay-based computer he dubbed the "Model K" (for “Kitchen", where he had assembled it), which calculated using binary addition. Bell Labs thus authorized a full research program in late 1938 with Stibitz at the helm.

History of Binary Numbers Their Complex Number Computer, completed January 8, 1940, was able to calculate complex numbers. In a demonstration to the American Mathematical Society conference at Dartmouth College on September 11, 1940, Stibitz was able to send the Complex Number Calculator remote commands over telephone lines by a teletype. It was the first computing machine ever used remotely over a phone line.

History of Binary Model K The first Relay Based Computer to use Binary Numbers (1937)

Decimal Number System Decimal notation is the writing of numbers in a base-10 numeral system. Examples are Roman numerals, Brahmi numerals, and Chinese numerals, as well as the Hindu-Arabic numerals used by speakers of English.

What is Binary The binary numeral system, or base-2 number system represents numeric values using two symbols (Numbers), usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.

Binary reads backwards Normally we count from left to right, 1 2 3 4 etc. In Binary we count in the opposite direction 8 4 2 1 It’s important to remember this in order to convert your numbers.

Why do we need to know about Binary? It is the building block of all data In order to understand storage capacity and sizes, you need to know how data is read and saved The data is fragile, each digit is need to be whole

Files Read/Write When you save a word document the computer will sequence the data in binary form. Each string of digits represent a certain value such as a letter, space, underlined etc. Each program has a certain way that it reads and writes data, all of it is written in Binary.

Understanding Binary Decimal 1 Binary 0001 off off off on

Understanding Binary Decimal 2 Binary 0010 off off on off

Understanding Binary Decimal 3 Binary 0011 off off on on

Understanding Binary Decimal 4 Binary 0100 off off on on

Understanding Binary Decimal 5 Binary 0101 off on off on

Understanding Binary 0101 off on off on

Each Number is doubled      128 64 32 16 8 4 2 1     2^8 2^6 2^5 2^4 2^3 2^2 2^1 2^0 Two to the power of three (2)(2)(2) 2*2*2 2X2X2 512 256 128 64 32 16 8 4 2 1 524288 262144 131072 65536 32768 16384 8192 4096 2048 1024 Technically, each level is 2 to the power 20 = 1 21 = 2 22 = 4 23 = 8 24 = 16 and so on (But essentially, since they are powers of 2, each new level is double (or 2 x) the previous)

Boardwork Lets express a few numbers in Binary: 130 25 43 85 1312 2204

Using Binary Coding Information Remember Bit = 0 or 1, Binary Digit Byte = the number of bits used to represent letters, numbers and special characters such as $ # , / &. 8 Bits = 1 Bytes Word = number of bytes a computer can process at one time by the CPU. So, Bits form Bytes and Bytes form Words.

Using Binary Coding Information Two common formats for coding letters, numbers and special characters are: EBCDIC -- Extended Binary Coded Decimal Interchange Code 8 bit code Originally used in IBM mainframes ASCII -- American Standard Code for Information Interchange 7 bit code Originally used on non-IBM systems

ASCII Binary Table