1 / 17

Section 4.4 Computation in Other Bases

Section 4.4 Computation in Other Bases. What You Will Learn. Performing addition, subtraction, multiplication and division in other bases. +. 0. 1. 2. 3. 4. 0. 0. 1. 2. 3. 4. 1. 1. 2. 3. 4. 10. 2. 2. 3. 4. 10. 11. 3. 3. 4. 10. 11. 12. 4. 4. 10. 11. 12. 13.

Download Presentation

Section 4.4 Computation in Other Bases

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Section 4.4Computation in Other Bases

  2. What You Will Learn • Performing addition, subtraction, multiplication and division in other bases

  3. + 0 1 2 3 4 0 0 1 2 3 4 1 1 2 3 4 10 2 2 3 4 10 11 3 3 4 10 11 12 4 4 10 11 12 13 Addition • An addition table can be made for any base and be used to add in that base. • Base 5 Addition Table

  4. Example 2: Using the Base 5 Addition Table Add 345 +235 Solution From the table 45 + 35 = 125. Record the 2 and carry the 1. 13 45 + 2 35 25

  5. Example 2: Using the Base 5 Addition Table Solution 13 45 + 2 35 Add the numbers in the second column 15 + 35 + 25 = 115 13 45 + 2 35 1 1 25 The sum is 1125.

  6. Subtraction • Subtraction can also be performed in other bases. • When you “borrow,” you borrow the amount of the base given in the subtraction problem. • If you are subtracting in base 5, when you borrow, you borrow 5. • If you are subtracting in base 12, when you borrow, you borrow 12.

  7. Example 6: Subtracting in Base 12 Subtract 91B12 –2A212 Solution In the units column: 11 – 2 = 9 Second column: 1 – 10, so we need to borrow: 1 + 12 = 13; 13 – 10 = 3 Third column: 9 becomes 8; 8 – 2 = 6 91B12 –2A212 63912

  8. Multiplication • Multiplication can be performed in bases other than 10. • In base 10, 4 × 3 means four groups of three units. • In base 5, 45 × 35 means four groups of three units. • (1+1+1)+(1+1+1)+(1+1+1)+(1+1+1) • Regroup into groups of five: • (1+1+1+1+1)+(1+1+1+1+1)+(1+1) • 45 × 35 = 225

  9. × 0 1 2 3 4 0 0 0 0 0 0 1 0 1 2 3 4 2 0 2 4 11 13 3 0 3 11 14 22 4 0 4 13 22 31 Multiplication • Multiplication table for the given base is extremely helpful. • Base 5 Multiplication Table

  10. Multiplication • However, it may be easier to multiply the values in the base 10 system and then change the product to base 5. • Multiplying 4 × 3 in base 10 gives 12. • Converting 12 from base 10 to base five gives 225.

  11. Example 8: Multiplying in Base 7 Multiply 437 × 257 • Solution 5 × 3 = 1510 = (2 × 7) + (1 × 1)= 217 Record the 1, carry the 2 24 37 × 2 55 1

  12. Example 8: Multiplying in Base 7 • Solution (5 × 4) + 2 = 2210 = (3 × 7) + (1 × 1)= 317 Record 31 24 37 × 2 55 311

  13. Example 8: Multiplying in Base 7 • Solution 2 × 3 = 610 = 67 Record 6 24 37 × 2 55 311 6

  14. Example 8: Multiplying in Base 7 • Solution 2 × 4 = 810 = (1 × 7) + (1 × 1)= 117 Record 11, and add in base 7 24 37 × 2 55 311 116 15017

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

  16. Example 10: Dividing in Base 8 Divide • Solution The multiples of 6 in base 8: • 68 × 18 = 68 68 × 28 = 148 • 68 × 38 = 228 68 × 48 = 308 • 68 × 58 = 368 68 × 68 = 448 • 68 × 78 = 528 • Quotient is 5368, remainder 58

  17. Example 10: Dividing in Base 8 Be careful when subtracting! We had to borrow when subtracting 6 from 0 and when subtracting 4 from 1. Remember that we borrow 108, which is the same as 8 in base 10. • Check • Does (5368 × 68) + 58= 40718? • 5368 • × 68 • 40648 + 58 = 40718True

More Related