4.4.0: Exercises — Read — Invisible Network

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For the following exercises, create the multiplication table for the given base.

Exercise \(\PageIndex{1}\)

base 5

Exercise \(\PageIndex{2}\)

base 3

Exercise \(\PageIndex{3}\)

base 16 (Hint: Use the digits \(0,1,2,3,4,5,6,7,8,9, A, B, C, D, E, F\).

Exercise \(\PageIndex{4}\)

base 2

For the following exercises, perform the indicated base 6 operation.

Exercise \(\PageIndex{5}\)

\(4_6 \times 3_6\)

Exercise \(\PageIndex{6}\)

\(14_6 \times 5_6\)

Exercise \(\PageIndex{7}\)

\(31_6 \times 3_6\)

Exercise \(\PageIndex{8}\)

\(43_6 \times 34_6\)

Exercise \(\PageIndex{9}\)

\(532_6 \times 23_6\)

Exercise \(\PageIndex{10}\)

\(254_6 \times 143_6\)

Exercise \(\PageIndex{11}\)

\(20_6 \div 36\)

Exercise \(\PageIndex{12}\)

\(23_5 \div 5_6\)

For the following exercises, perform the indicated base 12 operation.

Exercise \(\PageIndex{13}\)

\(5_{12} \times 6_{12}\)

Exercise \(\PageIndex{14}\)

\(3_{12} \times \mathrm{A}_{12}\)

Exercise \(\PageIndex{15}\)

\(34_{12} \times 7_{12}\)

Exercise \(\PageIndex{16}\)

\(76_{12} \times \mathrm{B}_{12}\)

Exercise \(\PageIndex{17}\)

\(59_{12} \times 1 \mathrm{~A}_{12}\)

Exercise \(\PageIndex{18}\)

\(\mathrm{A1}_{12} \times 36_{12}\)

Exercise \(\PageIndex{19}\)

\(53_{12} \div 9_{12}\)

Exercise \(\PageIndex{20}\)

\(2 \mathrm{~B}_{12} \div 7_{12}\)

Exercise \(\PageIndex{21}\)

Explain two ways to detect an error in arithmetic in bases other than base 10.

Exercise \(\PageIndex{22}\)

Explain the error in the following calculation: \(15_{12} \times 7_{12}=105_{12}\)

Exercise \(\PageIndex{23}\)

Explain the error in the following calculation: \(45_8 \times 6_8=94_8\).

Exercise \(\PageIndex{24}\)

In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 6 ?

Exercise \(\PageIndex{25}\)

In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 14 ?

Exercise \(\PageIndex{26}\)

In base 10 multiplication, there are 100 multiplication rules plus a rule for carrying a number. How many multiplication rules are there for base 2?

Exercise \(\PageIndex{27}\)

Consider the answers from Exercise 24 and Exercise 26. Which base do you think would be more efficient: base 10, base 6, or base 2?

For the following exercises, use the multiplication table that you created from Exercise 4 to perform the indicated base 2 operations.

Exercise \(\PageIndex{28}\)

\(11_2 \times 11_2\)

Exercise \(\PageIndex{29}\)

\(101_2 \times 10_2\)

Exercise \(\PageIndex{30}\)

\(11011_2 \times 1011_2\)

Exercise \(\PageIndex{31}\)

\(1011_2 \times 1010101_2\)

Exercise \(\PageIndex{32}\)

Convert \(1011_2\) and \(1010101_2\) to base 10. Then multiply those base 10 numbers. Next, convert the answer you got for Exercise 31 to base 10. Do these numbers match?

For the following exercises, use the multiplication table that you created from Exercise 3 to perform the indicated base 16 operations.

Exercise \(\PageIndex{33}\)

\(19_{16} \times 5_{16}\)

Exercise \(\PageIndex{34}\)

\(3 \mathrm{~B}_{16} \times \mathrm{A}_{16}\)

Exercise \(\PageIndex{35}\)

\(25_{16} \times 16_{16}\)

Exercise \(\PageIndex{36}\)

\(\mathrm{C}_{16} \div 4_{16}\)

For the following exercises, explain how you know an error was committed without performing the operation in the given base.

Exercise \(\PageIndex{37}\)

\(43_5 \times 32_5=126_5\)

Exercise \(\PageIndex{38}\)

\(5_{14} \times 9_{14}=45_{14}\)

4.4.0: Exercises is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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