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Binary Numbers and Conversions

Binary Numbers and Conversions. There are only 10 types of people in the world. Those that understand binary and those that don't. Binary Overview. Binary Numbers Overview

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Binary Numbers and Conversions

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  1. Binary Numbers and Conversions

  2. There are only 10 types of people in the world. Those that understand binary and those that don't.

  3. Binary Overview • Binary Numbers Overview • Binary is a number system used by digital devices like computers, cd players, etc. Binary is Base 2, unlike our counting system decimal which is Base 10 (denary). In other words, Binary has only 2 different numerals (0 and 1) to denote a value, unlike Decimal which has 10 numerals (0,1,2,3,4,5,6,7,8 and 9). Here is an example of a binary number: 10011100As you can see it is simply a bunch of zeroes and ones, there are 8 numerals in all which make this an 8 bit binary number. Bit is short for Binary Digit, and each numeral is classed as a bit. The bit on the far right, in this case a 0, is known as the Least significant bit (LSB). The bit on the far left, in this case a 1, is known as the Most significant bit (MSB)

  4. Binary Overview • Computers are unable to use our decimal system. • They can only handle signals that are either ON or OFF. • The binary system is perfect for this. • “1” represents ON, and “0” represents OFF. • So what a computer is saying for the number 101 is: block 4 ON, block 2 OFF, block 1 ON.

  5. Binary Numbers Electronically binary numbers are stored/processed using off or on electrical pulses, a digital system will interpret these off and on states as 0 and 1. In other words if the voltage is low then it would represent 0 (off state), and if the voltage is high then it would represent a 1 (on state).

  6. Binary Numbers • We ordinarily write numbers in base 10. • That means there are 10 digits, 0-9. • For example, consider 209 in ordinary base 10. • You know that is 2 hundreds, plus 0 tens, plus 9 ones. • Hundred, ten, and one are all powers of 10, our base. So we could think of it this way.

  7. Binary Numbers • Now we can easily use this same method to write numbers in base 2. • Instead of powers of 10, we use powers of 2, and remember we can only use 2 digits -- 0 and 1. • Let's convert 28 in base 10 to base 2. • So 28 in binary is 11100

  8. Converting To/From Binary • All you have to do is use the following table • So if you had the binary number of 132, that would be what?

  9. Binary Numbers • Lets try some together as a class. Click on the link below • http://www.wisc-online.com/objects/ViewObject.aspx?ID=DIG902 • Practice on your own • http://forums.cisco.com/CertCom/game/binary_game_page.htm

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