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The '''binary system''' is a way of representing numbers in base 2, i.e. using only the digits 0 and 1. The term 'Binary' means ''composed of two parts'' and comes from the Latin, originally meaning "two by two". Binary, or base 2, is one of many possible [[Number Systems]]. A number written in the system can be denoted by following it with a subscript 2, i.e. ₂. Each digit represents the number of a power of 2 in the complete number, similarly to in the [[decimal system]], where each digit represents the number of a power of 10. The power is defined by the number of digits in the number from right to left through the digit, minus 1, e.g. 100₂, where the digit 1 is the third digit from the right, and thus represents 2², or 4. While it is generally impractical for [[human]] use, it is the mainstay of modern [[computing]]. A binary system is also used in [[electronics]], which commonly uses '''0''' to mean "no voltage is present" '''1''' to mean "a voltage is present". Binary notation is used in circumstances in which a thing is in one of two possible conditions and no other condition is possible; the switch is on or the switch is off, the page has data on it or the page has no data. ==Operations== ===Successor Function===

1. #Current digit is the end digit 2. #Change the current digit 3. # If current digit = 1 4. ##Then: 4a.###Shift current digit to away from the end digit 4b.Goto ###Go to step 2 5: ##Else: 5a:###You're done. ===Addition=== Binary addition is fairly simple, making for efficient use in computers. To add one bit (digit) binary numbers, use the following table:{| class="wikitable"|-! X! Y! X + Y! Carry|-| 0| 0| 0| 0|-| 1| 0| 1| 0|-| 0| 1| 1| 0|-| 1| 1| 0| 1|-|} to add a multiple digit number, add the bits (digits) individually using the table, and add the carry if necessary. Consider the following example:  000000110- Previous Addition's carry 1000110110 X + 0110001010 Y----------------- 1110111000 ===Subtraction===Subtraction in binary can be carried out similar to decimal notation, however, there is a more efficient way, which is usually used in computers. Negative numbers a written in "Two's complement notation". In this notation, You "flip" the digits in the binary number and add one. For example, <blockquote>-10011 = 01100 + 1 = 01101</blockquote> To do subtraction, you add a number to its complement and ignore the final carry. <blockquote>5 - 2 = 101 - 010 = 101 + (101 + 1) = 101 + 110 = [1]011 = 011 = 3</blockquote> Note that this method requires the amount of digits to be fixed. ===Multiplication===Multiplication in binary is far more simple than multiplication in decimal. To multiply two binary numbers X * Y, use the following algorithm:#set a to 0#start at the rightmost digit of the X#for the nth digit (from the right, starting with 0)##If the digit is zero, continue##If the digit is one,###Append n zeros to the end of Y and add this to a#a is now equal to X * Y For Example: