Computation in Other Bases

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Presentation transcript:

Computation in Other Bases 4.4 Computation in Other Bases

Addition An addition table can be made for any base and it can be used to add in that base. Base 5 Addition Table 13 12 11 10 4 3 2 1 +

Example: Using the Base 5 Addition Table + 235 Solution: From the table 45 + 35 = 125. Record the 2 and carry the 1. 1445 + 235 25

Example: Using the Base 5 Addition Table continued Add the numbers in the second column, (15 + 45) + 25 = 105 + 25 = 125. Record the 12. 1445 + 235 1225 The sum is 1225.

Subtraction Subtraction can also be performed in other bases. When you “borrow” you borrow the amount of the base given in the subtraction problem. Example: If you are subtracting in base 5, when you borrow, you borrow 5.

Multiplication Multiplication table for the given base is extremely helpful. Base 5 Multiplication Table 31 22 13 4 14 11 3 2 1 

Example: Using the Base 5 Multiplication Table Multiply 125  35 Solution: Use the base 5 multiplication table to find the products. When the product consists of two digits, record the right digit and carry the left digit.

Example: Using the Base 5 Multiplication Table continued Record the 1 carry the 1. 1125  35 1 (35  15) + 15 = 45 Record the 4. 125  35 415 The product is 415.

Division Division is carried out much the same way as long division in base 10. A division problem can be checked by multiplication. (quotient  divisor) + remainder = dividend

Homework P. 198 # 9 – 54 (x3)