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Objective 1.1: Describe the binary numbering systemsResources:For this section you should have the following resources:
The BIT ( Binary Digit )A binary number, at its most basic level, is called a BIT ( BIT being short for BinarydigIT). A BIT is a value which can hold two possible states. These states can be many different things. They can be...
Numerically they are expressed as ONE (1) or ZERO (0). Every piece of information stored in a computer system ultimately breaks down to one of these two BITS. In digital electronics, these bits are represented by switching on or off a small amount of electric current to a device which is capable of sensing that current.
Logic ProbesSo there you have the basics of our entire information system revolution! The lonely little BIT. The instrument we use in Digital electronics to measure this binary digit is called the LOGIC PROBE. You will find a logic probe connection on your Vulcan trainer on the "header" socket shown attached to the green wire in the following illustration. A logic HIGH is shown as a RED lamp in the logic trainer, and a logic LOW is shown as a GREEN lamp. An absent logic level ( neither HIGH or LOW) is indicated by NO lamp lighting. The LOGIC PROBE connection Binary Weighted NumbersBinary values can represent conditions of various elements such as:
Any phenomenon which has two possible conditions may be represented by a BIT. You can also combine many bits together to create a number! If you need to have a computer recognize a quantity, you can place the bits in a sequence of "binary weighted numbers". This is called the Base2 numbering system. (Base 2 numbering system)Now, you may have noticed that the BIT doesn't carry much weight. Sure, it's fine if you want to describe one of two quantities like UP or DOWN, YES or NO. What do you do if you need more than that. How do you turn the bits into numbers? Well, you take a large number of bits, and turn them into something larger. You can take eight BITS, for instance, and create a number called a BYTE! Each bit in the byte represents a weighted value, and the value of that bit determines if that value should be included in the number or not. 0 means, don't include that weighting, 1 means DO include that weighting.
The weighting of the BIT increases by a factor of two from the BIT to it's right. Showing numbers in binary format is called the BASE2 numbering system. Click on image to download MMlogic simulation. Try clicking on the illustration above to download the Multimedia logic simulation. When you press any key on the keypad, the binary value which is associated with that number will show up on the lights. Remember, if the light is ON, then add on its associated weighting. A partial binary equivalence table is shown below...
For more information on binary numbering systems, try these sites... http://www.nwu.edu/musicschool/links/projects/midi/pages/undstdbh.html http://whatis.techtarget.com/WhatIs_Definition_Page/0,4152,213816,00.html http://www.usbyte.com/common/Binary%20System.htm
Base8 ( Octal ) Numbering systemMore to come: Until I can make it back to update this section, visit: http://whatis.techtarget.com/WhatIs_Definition_Page/0,4152,212687,00.html
Base16 ( Hexadecimal ) Numbering systemMore to come! In the meantime, visit these great links: http://webopedia.internet.com/TERM/h/hexadecimal.html http://ag.arizona.edu/classes/ABE547/lab4/HexadecimalCounting/ http://whatis.techtarget.com/WhatIs_Search_Results_Exact/1,282033,,00.html?query=hexadecimal
Converting between numbering systemsI'm off to do some work on the LOGIC GATES page... If you want to learn how to convert between numbering systems, try these links... http://jimvb.home.mindspring.com/binary.htm http://www.jaworski.com/htmlbook/dechex.htm http://www.cuttheknot.com/binary.html http://www.studdard.com/tutorial/base/binarycvt.html http://acc6.its.brooklyn.cuny.edu/~gurwitz/core5/nav2tool.html
