01.number systems

1. Number Systems Chapt. 2 Location in course textbook

Common Number Systems No No 0, 1, … 9, A, B, … F 16 Hexa- decimal No No 0, 1, … 7 8 Octal Yes No 0, 1 2 Binary No Yes 0, 1, … 9 10 Decimal Used in computers? Used by humans? Symbols Base System

Quantities/Counting (1 of 3) p. 33 7 7 111 7 6 6 110 6 5 5 101 5 4 4 100 4 3 3 11 3 2 2 10 2 1 1 1 1 0 0 0 0 Hexa- decimal Octal Binary Decimal

Quantities/Counting (2 of 3) F 17 1111 15 E 16 1110 14 D 15 1101 13 C 14 1100 12 B 13 1011 11 A 12 1010 10 9 11 1001 9 8 10 1000 8 Hexa- decimal Octal Binary Decimal

Quantities/Counting (3 of 3) Etc. 17 27 10111 23 16 26 10110 22 15 25 10101 21 14 24 10100 20 13 23 10011 19 12 22 10010 18 11 21 10001 17 10 20 10000 16 Hexa- decimal Octal Binary Decimal

Conversion Among Bases ,[object Object],Hexadecimal Decimal Octal Binary pp. 40-46

Quick Example 25 10 = 11001 2 = 31 8 = 19 16 Base

Decimal to Decimal (just for fun) Hexadecimal Decimal Octal Binary Next slide…

125 10 => 5 x 10 0 = 5 2 x 10 1 = 20 1 x 10 2 = 100 125 Base Weight

Binary to Decimal Hexadecimal Decimal Octal Binary

Binary to Decimal ,[object Object],[object Object],[object Object],[object Object]

Example 101011 2 => 1 x 2 0 = 1 1 x 2 1 = 2 0 x 2 2 = 0 1 x 2 3 = 8 0 x 2 4 = 0 1 x 2 5 = 32 43 10 Bit “0”

Octal to Decimal Hexadecimal Decimal Octal Binary

Octal to Decimal ,[object Object],[object Object],[object Object],[object Object]

Example 724 8 => 4 x 8 0 = 4 2 x 8 1 = 16 7 x 8 2 = 448 468 10

Hexadecimal to Decimal Hexadecimal Decimal Octal Binary

Hexadecimal to Decimal ,[object Object],[object Object],[object Object],[object Object]

Example ABC 16 => C x 16 0 = 12 x 1 = 12 B x 16 1 = 11 x 16 = 176 A x 16 2 = 10 x 256 = 2560 2748 10

Decimal to Binary Hexadecimal Decimal Octal Binary

Decimal to Binary ,[object Object],[object Object],[object Object],[object Object],[object Object]

Example 125 10 = ? 2 125 10 = 1111101 2 2 125 62 1 2 31 0 2 15 1 2 7 1 2 3 1 2 1 1 2 0 1

Octal to Binary Hexadecimal Decimal Octal Binary

Octal to Binary ,[object Object],[object Object]

Example 705 8 = ? 2 705 8 = 111000101 2 7 0 5 111 000 101

Hexadecimal to Binary Hexadecimal Decimal Octal Binary

Hexadecimal to Binary ,[object Object],[object Object]

Example 10AF 16 = ? 2 10AF 16 = 0001000010101111 2 1 0 A F 0001 0000 1010 1111

Decimal to Octal Hexadecimal Decimal Octal Binary

Decimal to Octal ,[object Object],[object Object],[object Object]

Example 1234 10 = ? 8 8 1234 154 2 1234 10 = 2322 8 8 19 2 8 2 3 8 0 2

Decimal to Hexadecimal Hexadecimal Decimal Octal Binary

Decimal to Hexadecimal ,[object Object],[object Object],[object Object]

Example 1234 10 = ? 16 1234 10 = 4D2 16 16 1234 77 2 16 4 13 = D 16 0 4

Binary to Octal Hexadecimal Decimal Octal Binary

Binary to Octal ,[object Object],[object Object],[object Object]

Example 1011010111 2 = ? 8 1011010111 2 = 1327 8 1 011 010 111 1 3 2 7

Binary to Hexadecimal Hexadecimal Decimal Octal Binary

Binary to Hexadecimal ,[object Object],[object Object],[object Object]

Example 1010111011 2 = ? 16 ,[object Object],[object Object],1010111011 2 = 2BB 16

Octal to Hexadecimal Hexadecimal Decimal Octal Binary

Octal to Hexadecimal ,[object Object],[object Object]

Example 1076 8 = ? 16 1076 8 = 23E 16 1 0 7 6 001 000 111 110 2 3 E

Hexadecimal to Octal Hexadecimal Decimal Octal Binary

Hexadecimal to Octal ,[object Object],[object Object]

Example 1F0C 16 = ? 8 1F0C 16 = 17414 8 1 F 0 C 0001 1111 0000 1100 1 7 4 1 4

Exercise – Convert ... Skip answer Answer Don’t use a calculator! 1AF 703 1110101 33 Hexa- decimal Octal Binary Decimal

Exercise – Convert … Answer 1AF 657 110101111 431 1C3 703 111000011 451 75 165 1110101 117 21 41 100001 33 Hexa- decimal Octal Binary Decimal

Common Powers (1 of 2) ,[object Object],T tera 10 12 G giga 10 9 M mega 10 6 k kilo 10 3 m milli 10 -3  micro 10 -6 n nano 10 -9 p pico 10 -12 Symbol Preface Power 1000000000000 1000000000 1000000 1000 .001 .000001 .000000001 .000000000001 Value

Common Powers (2 of 2) ,[object Object],[object Object],[object Object],G Giga 2 30 M mega 2 20 k kilo 2 10 Symbol Preface Power 1073741824 1048576 1024 Value

Example In the lab… 1. Double click on My Computer 2. Right click on C: 3. Click on Properties / 2 30 =

Exercise – Free Space ,[object Object],etc. E: D: C: A: GB Bytes Drive Free space

Review – multiplying powers ,[object Object],2 6  2 10 = 2 16 = 65,536 or… 2 6  2 10 = 64  2 10 = 64k a b  a c = a b+c

Binary Addition (1 of 2) ,[object Object],pp. 36-38 “two” 10 1 1 1 0 1 1 1 0 0 0 0 A + B B A

Binary Addition (2 of 2) ,[object Object],[object Object],[object Object],[object Object],10101 21 + 11001 + 25 101110 46 1 1

Multiplication (1 of 3) ,[object Object],pp. 39 35 x 105 175 000 35 3675

Multiplication (2 of 3) ,[object Object],1 1 1 0 0 1 0 1 0 0 0 0 A  B B A

Multiplication (3 of 3) ,[object Object],[object Object],[object Object],1110 x 1011 1110 1110 0000 1110 10011010

Fractions ,[object Object],pp. 46-50 3.14 => 4 x 10 -2 = 0.04 1 x 10 -1 = 0.1 3 x 10 0 = 3 3.14

Fractions ,[object Object],pp. 46-50 10.1011 => 1 x 2 -4 = 0.0625 1 x 2 -3 = 0.125 0 x 2 -2 = 0.0 1 x 2 -1 = 0.5 0 x 2 0 = 0.0 1 x 2 1 = 2.0 2.6875

Fractions ,[object Object],p. 50 3.14579 .14579 x 2 0.29158 x 2 0.58316 x 2 1.16632 x 2 0.33264 x 2 0.66528 x 2 1.33056 etc. 11.001001...

Exercise – Convert ... Skip answer Answer Don’t use a calculator! C.82 3.07 101.1101 29.8 Hexa- decimal Octal Binary Decimal

Exercise – Convert … Answer C.82 14.404 1100.10000010 12.5078125 3.1C 3.07 11.000111 3.109375 5.D 5.64 101.1101 5.8125 1D.CC… 35.63… 11101.110011… 29.8 Hexa- decimal Octal Binary Decimal

01.number systems

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