Presentation on theme: "Calculating in Other Bases"— Presentation transcript:
1 Calculating in Other Bases Section 4.3Calculating in Other Bases
2 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.
3 Key TermsDigital – 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.
4 BackgroundAs 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.
5 Base TenBase TwoBase FiveBase EightBase Sixteen121031141005101611071111281000139100114101020A101121B110022C11012315D11102416E11113017F100003110001321810010331910011341010040
6 Example 1: 245List the number before and after the given number, in the given base.
7 Example 2: 2045List the number before and after the given number, in the given base.
8 Example 3: 678List the number before and after the given number, in the given base.
9 Example 4: 1916List the number before and after the given number, in the given base.
10 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.
11 Example 5: 245Convert to decimal (base ten) notation.
12 Example 6: 40,3125Convert to decimal (base ten) notation.
13 Example 7: 7,0368Convert to decimal (base ten) notation.
14 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.
15 Example 8: 384Convert from decimal to base 5 Notation.
16 Example 9: 645Convert from decimal to base 5 Notation.
17 Example 10: 1838Convert from decimal to base 6 Notation.
18 Section 4.3 AssignmentClass work:Worksheet on teacher website
19 Section 4.3 Part IIAdding, Subtracting, Multiplying, and Dividing in Other Bases
20 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.”