4.4 Perform Computations in Other Bases 199 The product of × 4 3 ,or22 , 5 5 5 is circled in Table 4.9, the base 5 multiplication table. We can construct other values in the base 5 multiplication table in the same way. You may, however, find it easier to multiply the values in the base 10 system and then change the product to base 5 by using the procedure discussed in Section 4.3. Multiplying × 4 3 in base 10 gives 12, and converting 12 from base 10 to base 5 gives 22 .5 The other values in the table may be determined by either method discussed. Table 4.9 Base 5 Multiplication Table × 0 1 2 3 4 0 0 0 0 0 0 1 0 1 2 3 4 2 02 41113 3 0 3 11 14 22 4 0 4 13 22 31 Addition and Multiplication in Base 5 Example 7 Using the Base 5 Multiplication Table Multiply × 13 3 5 5 Solution Use the base 5 multiplication table to determine the products. When the product consists of two digits, record the right digit and carry the left digit. Multiplying gives × = 3 3 14 . 5 5 5 Record the 4 and carry the 1. × 13 3 4 1 5 5 × + = (3 1 ) 1 4 . 5 5 5 5 Record the 4. × 13 3 44 1 5 5 5 The product is 44 .5 7 Now try Exercise 31 Constructing a multiplication table is often tedious, especially when the base is large. To multiply in a given base without the use of a table, multiply in base 10 and convert the products to the appropriate base before recording them. This procedure is illustrated in Example 8. Example 8 Multiplying in Base 7 Multiply 43 25 7 7 × Solution × = = × + × = 53 15 (2 7) (11) 21. 10 7 Record the 1 and carry the 2. 43 25 1 2 7 7 × ×+= += =×+×= (5 4) 2 20 2 22 (3 7) (11) 31. 10 7 Record the 31. 43 25 311 2 7 7 × × = = 2 3 6 6 . 10 7 Record the 6. × 43 25 311 6 2 7 7 Learning Catalytics Keyword: Angel-SOM-4.4 (See Preface for additional details.)
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