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**Calculating in Other Bases**

Section 4.3 Calculating in Other Bases

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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 1 2 10 3 11 4 100 5 101 6 110 7 111 12 8 1000 13 9 1001 14 1010 20 A 1011 21 B 1100 22 C 1101 23 15 D 1110 24 16 E 1111 30 17 F 10000 31 10001 32 18 10010 33 19 10011 34 10100 40

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Example 1: 245 List the number before and after the given number, in the given base.

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Example 2: 2045 List the number before and after the given number, in the given base.

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Example 3: 678 List the number before and after the given number, in the given base.

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Example 4: 1916 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: 245 Convert to decimal (base ten) notation.

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Example 6: 40,3125 Convert to decimal (base ten) notation.

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Example 7: 7,0368 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**

+ 1 2 3 4

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Example 11: Adding Base 5

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Example 12: Adding Base 6 + 1 2 3 4 5

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**Example 13: Subtracting Base 5**

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**Example 14: Subtracting Base 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**

X 1 2 3 4

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**Example 15: Multiplying Base 5**

345 x 425…..Use Galley Method

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**Example 16: Multiplying Base 5**

1345 x 325…..Use Galley Method

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**Example 17: Division in Base 5**

41325 235……..1st need to know multiples of 235

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**Example 18: Division in Base 5**

21435 325……..1st need to know multiples of 325

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**Binary, Octal, and Hexadecimal Notation**

Base Ten Base Two Base Eight Base Sixteen 1 2 10 3 11 4 100 5 101 6 110 7 111 8 1000 9 1001 1010 12 A 1011 13 B 1100 14 C 1101 15 D 1110 16 E TB pg. 226

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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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