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Calculating in Other Bases Section 4.3

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Objectives Change numerals in bases other than ten to base ten. Change base ten numerals to numerals in other bases. Add and Subtract in bases other than ten. Multiply and Divide in bases other than ten.

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Key Terms Digital – a word used in computer technology and refers to a method of encoding numbers, letters, visual images, and sounds using a base two system. Binary – base two system. Octal System – base eight. Hexadecimal System – base sixteen.

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Background As you have seen, so far, most numeral systems are based on powers of ten, except for the Babylonian and Mayan system. Babylonian system based on powers of 60. Mayan system based on powers of 20. Other societies around the world, including ours, use bases 2, 3, 4, 5, or 8. Computers, DVD players, and cell phones use bases 2, 8, and 16.

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Base Ten Base Two Base Five Base Eight Base Sixteen 00000 11111 210222 311333 4100444 51011055 61101166 71111277 8100013108 9100114119 1010102012A 1110112113B 1211002214C 1311012315D 1411102416E 1511113017F 1610000312010 1710001322112 1810010332213 1910011342314 2010100402415

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Example 1: 24 5 List the number before and after the given number, in the given base.

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Example 2: 204 5 List the number before and after the given number, in the given base.

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Example 3: 67 8 List the number before and after the given number, in the given base.

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Example 4: 19 16 List the number before and after the given number, in the given base.

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Section 4.3 Assignment Class work: TB pg. 228/1 – 10 Remember you must write the problem and show ALL work, when necessary, to receive credit for the assignment.

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Example 5: 24 5 Convert to decimal (base ten) notation.

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Example 6: 40,312 5 Convert to decimal (base ten) notation.

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Example 7: 7,036 8 Convert to decimal (base ten) notation.

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Section 4.3 Assignment Class work: TB pg. 228/12 – 22 Remember you must write problems and show ALL work to receive credit for the assignment.

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Example 8: 384 Convert from decimal to base 5 Notation.

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Example 9: 645 Convert from decimal to base 5 Notation.

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Example 10: 1838 Convert from decimal to base 6 Notation.

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Section 4.3 Assignment Class work: Worksheet on teacher website

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Section 4.3 Part II Adding, Subtracting, Multiplying, and Dividing in Other Bases

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NOTE: “If you thoroughly understand the concept of place value in our Hindu-Arabic numeration system, then you can easily modify the techniques…to compute in other place value systems.”

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Addition Table for Base 5 +01234 0 1 2 3 4

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Example 11: Adding Base 5 342 5 +223 5

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Example 12: Adding Base 6 315 6 +524 6 +012345 0 1 2 3 4 5

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Example 13: Subtracting Base 5 424 5 - 143 5

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Example 14: Subtracting Base 6 325 6 - 131 6

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Section 4.3 Assignment II Class work: TB pg. 229/44 – 56 Even Remember you must write problems and show ALL work to receive credit for this assignment.

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Multiplication Table for Base 5 X01234 0 1 2 3 4

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Example 15: Multiplying Base 5 34 5 x 42 5 …..Use Galley Method

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Example 16: Multiplying Base 5 134 5 x 32 5 …..Use Galley Method

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Example 17: Division in Base 5 4132 5 23 5 ……..1 st need to know multiples of 23 5

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Example 18: Division in Base 5 2143 5 32 5 ……..1 st need to know multiples of 32 5

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Binary, Octal, and Hexadecimal Notation TB pg. 226 Base Ten Base Two Base Eight Base Sixteen 0000 1111 21022 31133 410044 510155 611066 711177 81000108 91001119 10101012A 11101113B 12110014C 13110115D 14111016E

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Section 4.3 Assignment II Class work: Worksheet Online Multiplying and Dividing in other Bases Remember you must show ALL work to receive credit for the assignment.

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