4.4 Perform Computations in Other Bases 197 You can develop an addition table for any base and use it to add in that base. As you get more comfortable with addition in other bases, however, you may prefer to add in other bases by using mental arithmetic. To do so, convert the sum from the given base to base 10 and then convert the base 10 numeral back into the given base. You must clearly understand how to convert from base 10 to the given base, as discussed in Section 4.3. For example, to add + 7 8 , 9 9 add + 7 8 in base 10 to get 1510 and then mentally convert 1510 to 169 using the procedure given earlier. Remember, 169 when converted to base 10 becomes × + × (1 9) (6 1), or 15. Addition using this procedure is illustrated in Example 4. Add the numbers in the second column, (1 3 ) 2 4 2 11 . 5 5 5 5 5 5 + + = + = Record the 11. 3 4 2 3 11 2 1 5 5 5 + The sum is 112 .5 7 Now try Exercise 9 Example 3 Add in Base 5 Add + 3214 2011 5 5 Solution 3 2 14 2 0 11 10 2 30 1 5 5 5 + The sum is 10230 .5 7 Now try Exercise 11 Example 4 Adding in Base 10; Converting to Base 4 Add + 1321 1133 4 4 Solution To solve this problem, make the necessary conversions by using mental arithmetic. + = = 1 3 4 10 . 10 4 Record the 0 and carry the 1. 1 3 21 1 1 33 0 1 4 4 4 + + + = = 1 2 3 6 12 . 10 4 Record the 2 and carry the 1. 1 3 2 1 11 33 2 0 1 1 4 4 4 + + + = = 1 3 1 5 11 . 10 4 Record the 1 and carry the 1. 1 3 2 1 1 1 33 1 2 0 1 1 1 4 4 4 + + + = = 1 1 1 3 3 . 10 4 Record the 3. 1 3 2 1 1 1 3 3 3 1 2 0 4 4 4 + The sum is 3120 .4 7 Now try Exercise 15
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