1 / 15

4.3

4.3. Computation in Positional Systems. Objectives Add in bases other than ten. Subtract in bases other than ten. Multiply in bases other than ten. Divide in bases other than ten. 2. Addition in Base 10. Add: 478 + 635. Example 1: Addition in Base Four. Add

nathanielcharles
Télécharger la présentation

4.3

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. 4.3 Computation in Positional Systems

  2. Objectives Add in bases other than ten. Subtract in bases other than ten. Multiply in bases other than ten. Divide in bases other than ten. 2

  3. Addition in Base 10 Add: 478 + 635

  4. Example 1: Addition in Base Four Add Solution:We add the right-hand column: 3four+3four=6ten. In base four, the digit symbols are 0, 1, 2, and 3. Since the sum exceeds 3, then we convert this base ten number, 6, to base four: 4

  5. Example 1 continued Record the sum in the right-hand column. Next, add the three digits in the fours’ column: 1four + 3four + 1four = 5ten 5 is not a digit symbol in base four, so, we must convert 5 into base four. 5

  6. Example 1 continued Record the 11four You can check by converting 33four, 13four, and 112four to base ten and taking the sum of 33four & 13four and make sure it is equal to112four. We leave this to the student. 6

  7. Subtract Base 10 Subtract 723 - 385

  8. Example 3: Subtraction in Base Four Subtract: Solution: Subtract the right column: 1four – 2four. Since 2four is larger than 1four, we borrow from the preceding column: 8

  9. Example 3 continued Next, subtract the second column from the right. Again, you can check by converting 31four, 12four, and 13four to base ten and taking the difference of 31four & 12four and making sure it is equal to13four. We leave this to the student. 9

  10. Multiply Base 10 Multiply: 371 x 28

  11. Example 5: Multiplication in Base Six Multiply: Solution:Multiply as we do in base ten. That is, multiply the digit 2 by the digit 4. 2six× 4six = 8ten = (1× 6) + (2 ×1) = 12six Record the 2 and carry the 1: 11

  12. Example 5 continued Next, we must involve both multiplication and addition: (2six× 3six) + 1six = 6 + 1 = 7ten = (1 × 6) + (1 × 1) = 11six. Record the 11six in the multiplication problem. As before, we can check this by converting to base ten. This is left to the student. 12

  13. Division Base 10 Divide:

  14. Example 6: Division in Base Four Use the table, showing products in base four, to perform the following division: Solution: Divide 22four by 3four. Use the table to find what times 3four is less than or equal to 22four. So, 14

  15. Example 6 continued Multiply 3four× 3four = 21four and write the product under the first two digits of the dividend. Subtract: 22four – 21four = 1four Bring down the next digit, 2four. Use the table to find what times 3four is less than or equal to 12four. We see 2four × 3four = 12four, so the quotient is 32four. 15

More Related