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<Title><![CDATA[Systems - Lesson 4: Arithmetic Algorisms in Different Bases]]></Title>
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<Title><![CDATA[Arithmetic Algorithms in Different Bases]]></Title>
<Notes><![CDATA[Text  Chapter 4   Section 4]]></Notes>
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<SlideText><![CDATA[Arithmetic Algorithms in Different Bases Addition, Subtraction, Multiplication and Division Text  Chapter 4   Section 4 ]]></SlideText>
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<Title><![CDATA[The Addition Algorithm]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[The Addition Algorithm To add in any base   Step 1 Add the digits in the  ones  column to find the number of  1s . If the number is less than the base place the number under the right hand column. If the number is greater than or equal to the base, express the number as a base numeral.  The first digit indicates the number of the base in the sum so carry that digit to the  base  column and write the second digit under the right hand column.       14    + 32  5  2 + 4 = 6 6 > 5  6 = 11 5 Place 1 under  4 + 2 and carry the 1 five to the  fives  column                      No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[Addition Algorithm - continued]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 1]]></Notes>
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<SlideText><![CDATA[Addition Algorithm - continued Step 2 Add the digits in the  base  column. If the sum is less than the base enter under the  base  column. If the sum is greater than or equal to the base express the sum as a base numeral.  Carry the first digit to the  base squared  column and place the second digit under the  base  column.   Step 3 Repeat this process to the end.     1      14   + 32  5            1 1+1+3 = 5 5 = 10 5  Carry the 1 five to the 52 column. Place 0 under the  five  column The sum is 101 5 In-class Assignment 20 - 1 ]]></SlideText>
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<Title><![CDATA[Example of Addition]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 1]]></Notes>
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<SlideText><![CDATA[Example of Addition  Find:    1          123         123          342 6          342 6               5           0 5                   1    1             123         342 6              5056 3 +  2 = 5 < 6 ’!no  6 s to carry.  2 + 4 = 6    6 = 10 6     One 6 2 to carry.     0 to go in the 6       column.  1 + 1 + 3 = 5 < 6 ’! no 62 to carry.  In-class Assignment 20 - 1 ]]></SlideText>
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<Title><![CDATA[The Subtraction Algorithm]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[The Subtraction Algorithm  Subtraction in any base, b Start as  1 s column. If the subtraction is possible enter the number under the  1 s column. If the subtraction is not possible borrow 1 of the groups of b in the minuend. The one b being borrowed is worth b in the  1 s column so add b to the digit in the minuend in the  1 s column . Continue in this manner through the problem No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[A Subtraction Problem]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 2]]></Notes>
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<SlideText><![CDATA[A Subtraction Problem  	 2"4  can not do. Borrow 1 of the 5  7 s in the minuend and add 7 to the 2  then subtract. 2"4 = 2 3"1 = 2  In-class Assignment 20 - 2 ]]></SlideText>
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<Title><![CDATA[Another Subtraction Problem]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 2]]></Notes>
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<SlideText><![CDATA[Another Subtraction Problem   ]]></SlideText>
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<Title><![CDATA[The Multiplication Algorithm]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[The Multiplication Algorithm To Multiply in any base The multiplication algorithm is the same as in base 10.  Things you need to remember. Carry groups of the base Indent for each multiplication row Add in the base ]]></SlideText>
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<Title><![CDATA[Multiplying in Base 3]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 3]]></Notes>
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<SlideText><![CDATA[Multiplying in Base 3                               2 x 2 = 4 = 11 3 Remember to  indent Add in base 3 ]]></SlideText>
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<Title><![CDATA[Carrying in Multiplication]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 3]]></Notes>
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<SlideText><![CDATA[Carrying in Multiplication                                                                             2 x 5 =10 =146  2 x 4 =8,  8 +1 =9 9 = 1 3 6 2 x 2 =4,  4 + 1 =5, 5 = 5 6 In-class Assignment 20 - 3 ]]></SlideText>
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<Title><![CDATA[The Division Algorithm]]></Title>
<Notes><![CDATA[No in-class assignment problem]]></Notes>
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<SlideText><![CDATA[The Division Algorithm To divide in any base The division algorithm in any base is the same as in base 10.  Things to remember   Digits that are entered in the quotient are at first estimates. Do all the multiplications on the side so that the digits used are not estimates. Multiply and subtract in the base used in the problem.   No in-class assignment problem ]]></SlideText>
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<Title><![CDATA[A Division Problem]]></Title>
<Notes><![CDATA[In-class Assignment 20 - 4]]></Notes>
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<SlideText><![CDATA[A Division Problem                                  1 x 45 =  45 2 x 45 = 135 3 x 45 = 225  4 x 45 = 315  0 x 45 =0 Subtract in base 5 3 x 45 =225 In-class Assignment 20 - 4 ]]></SlideText>
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