Download presentation

Presentation is loading. Please wait.

Published byChelsea Wilbur Modified over 2 years ago

1
© 2003 Dr. Kevin Chouinard Edited by Jean Pacelli 20041 Section 4.3 Converting Between Number Bases

2
2 Place Values for the Decimal System Also Called Base Ten __ __ __ thousandshundreds 10º tensones 10¹10²10³10 4 ten thousands 10 5 hundred thousands Digits for Base Ten 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

3
3 Value of a multi-digit number in Base Ten The base ten number 406,391 is 6 digits long, and is written in standard form. It is read four hundred and six thousand, three hundred ninety one. In expanded form, 406,391 = (4x10 5 ) + (0x10 4 ) + (6x10 3 ) + (3x10 2 ) + (9x10 1 ) + (1x10 0 ) = 4x100,000 + 0x10,000 + 6x1,000 + 3x100 + 9x10 + 1x1 This number system is multiplicative, and positional. The digit is in a specific place value, and is the multiplier for that place value. The 4 in the number 4000 has a different value from the 4 in the number 400.

4
4 Using Other Bases When we work in a base other than base 10, we must calculate the place values for that base. The place values will be powers of the base, starting with the 0 th power, 1 st power, 2 nd power, etc… working from right to left.

5
5 Place Values for Base Five Let’s try counting in base five. First, we need the place values. _ _ _ _ _ _ twenty- fives fivesones 5¹5¹5²5²5º5º

6
6 Counting in Base Five _ _ _ _ _ _ twenty- fives fivesones 5¹5¹5²5²5º5º 242322212014131211104321Base 5 1413121110987654321Base 10 10210110044434241403433323130Base 5 27262524232221201918171615Base 10

7
7 Conversion from base 5 to base 10 1432 five = _____ ten Answer: 1 5³ 4 5² 3 5¹ +2 5º 1 125 4 25 3 5 +2 1 125 100 15 + 2 242 ten

8
8 Conversion from base 10 to base 5 698 ten = _____ five Answer: Start by finding the powers of five which are 698 5º = 1 5¹ = 5 5² = 25 5³ = 125 How many 625’s are there in 698? 698 625 = 1 (R 73) How many 125’s are there in 73? 73 125 = 0 (R 73) How many 25’s are there in 73? 73 25 = 2 (R 23) How many 5’s are there in 23? 23 5 = 4 (R 3) How many 1’s are there in 3? 3 1 = 3 (R 0) 698 ten = 10243 five

9
9 Place Values for Base Eight Let’s examine the first four place values for base eight _ _ _ __ five- hundred- twelves sixty- fours 8º8º eightsones 8¹8¹8²8²8³8³

10
10 Conversion from base 8 to base 10 270 eight = _____ ten Answer: 2 8² 7 8¹ +0 8º 2 64 7 8 +0 1 128 56 + 0 184 ten

11
11 Conversion from base 10 to base 8 497 ten = _____ eight Answer: Start by finding the powers of eight which are 497 8º = 1 8¹ = 8 8² = 64 8³ = 512 How many 64’s are there in 497? 497 64 = 7 (R 49) How many 8’s are there in 49? 49 8 = 6 (R 1) How many 1’s are there in 1? 1 1 = 1 (R 0) 497 ten = 761 eight

12
12 Place Values for Base Two Let’s examine the first four place values for base two _ _ _ __ eightsfours 2º2º twosones 2¹2¹2²2²2³2³

13
13 Conversion from base 2 to base 10 1011 two = _____ ten Answer: 1 2³ 0 2² 1 2¹ +1 2º 1 8 0 4 1 2 +1 1 8 0 2 + 1 11 ten

14
14 Octal (base eight) 0 1 2 3 4 5 6 7 Binary (base two) 000 001 010 011 100 101 110 111 Binary to Octal Conversion

15
15 Examples 101110001 two = 561 eight 11011 two = 011011 two = 33 eight

16
16 Place Values for Base Sixteen Let’s examine the first four place values for base sixteen _ _ _ _ 4096256 16º sixteenones 16¹16²16³

17
17 Digits in various bases Base 100, 1, 2, 3, 4, 5, 6, 7, 8, 9 Base 80, 1, 2, 3, 4, 5, 6, 7 Base 50, 1, 2, 3, 4 Base 20, 1 Base 160, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

18
18 Digits in various bases (cont.) Note that each base has digits from 0 up to a number one less than the base Also, note that in base 16, A = 10 B = 11 C = 12 D = 13 E = 14 F = 15

19
19 Binary to Hexadecimal Conversion Hexadecimal (Base 16) 0 1 2 3 4 5 6 7 8 9 A B C D E F Binary (Base 2) 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111

20
20 Convert to base 10 423 five 317 eight 1010111 two = 113 ten = 207 ten = 87 ten

21
21 Convert to the indicated base 21 ten to base two 396 ten to base eight 392 ten to base five = 10101 two = 614 eight = 3032 five

22
22 Cereal Box Magic Trick

Similar presentations

OK

Number Systems & Binary How to count. How do we represent numbers? Early systems: – Actual count : ||||| = 5 – Roman numers : XI = 11 Hard to do math:

Number Systems & Binary How to count. How do we represent numbers? Early systems: – Actual count : ||||| = 5 – Roman numers : XI = 11 Hard to do math:

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Marketing mix ppt on nokia phones Ppt on earth dam breach Ppt on employee motivation Ppt on boiler used in sugar factory Ppt on carbon and its compounds model Ppt on brand building strategy Ppt on blood stain pattern analysis definition Skill based pay ppt online Ppt on 555 timer schematic Ppt on summary writing lesson