# Binary Arithmetic

May 13th, 2015
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Rules for addition, subtraction, and multiplication. The basic rules for binary subtraction are listed in the table below.

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Binary ArithmeticBinary ArithmeticRules for addition, subtraction, and multiplicationOperationResultCarryAddition0+00+11+01+101100001Subtraction0-00-11-01-101100100Multiplication0001101100010000Decimal0123010001Binary00000001001000111Decimal45671010001+Binary010001010110011101011111110+ Examples:10011001011100011111011001011100001++61117221133++ Class work1) 10001 + 11101 =2) 101101 + 11001 =3) 1011001 + 111010 =4) 1110 + 1111 =5) 10111 + 110101 =6) 11011 + 1001010 = Binary SubtractionThe basic rules for binary subtraction are listed in the table below.Rule 1Rule 2000110Rule 3101Rule 4011Again we see that the first three rules are similar to their decimal counterparts. The fourth rule, however, needs a little more explanation since it defines how we borrow fromanother column. Example (1):10011010110111110 11 01 1borrowsborrows Example (2):1101011001- 00101110101. Complement the second row and add:1101011001+ 1101000101(1)1010011110Now you notice that there is an embarrassing (1) at the left of the row. The rule now is to take this 1 across to the first column on the right and add it there, as shown below:10100111101+1010011111 Class work1) 1011011 10010 =2) 1010110 101010 =3) 1000101

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