Homework for the sixth week: numbers and computing

Practice is absolutely critical in this class.

Groups are fine, turn in your own work. Homework is due in or before class on Mondays.

- Section 4.1:
- Problems 35, 36 (the algorithm is in the text, see Section 4.1, Example 4)

- Section 4.2:
- Problems 2, 3, 5, 6, 11, 12

- Section 4.3:
- Problem 2, 7, 8
- Problems 19-22 (the “calculator shortcut” is Horner’s rule)
- Problems 37-40
- Problem 57 (he played at the festival)

- Expressing numbers in positional form:
- Take a familiar incomplete integer, -679-, and express it as a sum of the digits times powers of ten using variables {x}_{0} and {x}_{4} for the digits in the blanks. Simplify to the form of {x}_{4} ⋅ 1{0}^{4} + {x}_{0} ⋅ 1{0}^{0} + z, where z is a single number in positional form (a sequence of digits). Does 72 divide z? Does 8 divide z? Does 9 divide z? Remember that 72 = 8 ⋅ 9. We will use this example again in the next chapter.

- Operations;
- Multiply 47 by each of 3, 13, and 23. Show your work, and work digit-by-digit. Use either the expanded form (expanding (4 ⋅ 10 + 7) ⋅ (2 ⋅ 10 + 3) or the tabular form collapsing the sum every two steps.
- Add 47 to each of 52, 53, and 54. Show your work, and work digit-by-digit. Show an intermediate redundant representation if there is one.
- Subtract 19 from each of 7, 19 (not a typo), 20, and 29. Show your work, and work digit-by-digit. Show an intermediate redundant representation if there is one.

Note that you may email homework. However, I don’t use Microsoft^{TM} products
(e.g. Word), and software packages are notoriously finicky about translating
mathematics.

If you’re typing it (which I advise just for practice in whatever tools you use), you likely want to turn in a printout. If you do want to email your submission, please produce a PDF or PostScript document.