Number system | Representation and conversion | low level programming
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This document discusses different number systems used in digital electronics including decimal, binary, octal, and hexadecimal. It provides examples of numbers represented in each system and methods to convert between the different bases. Conversion methods covered include converting from binary, octal, or hexadecimal to decimal and vice versa, as well as converting between octal and hexadecimal to binary and back. Examples are given to demonstrate each conversion method.
Number system | Representation and conversion | low level programming
- 1. Department of Mechanical Engineering NIT, ARUNACHAL PRADESH Number System (Representation and Conversion)
- 3. NUMBER SYSTEM IN DIGITAL ELECTRONICS 1. Decimal Number 2. Binary Number 3. Octal Number 4. Hexadecimal Number 5. BCD Number 6. Excess 3 Code Used by Humans Used by Computer Digital System
- 4. COMMON NUMBER SYSTEM Number Base Allowable Digits / Characters Symbol Decimal (D) 10 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 … 10 Binary (B) 2 0, 1 … 2 Octal (O) 8 0, 1, 2, 3, 4, 5, 6, 7 … 8 Hexadecimal (H) 16 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F … 16
- 5. CONVERSION 1. B / O / H D 2. D B / O / H 3. O / H B H / O Decimal Hexadecimal Octal Binary 0 0 0 0 1 1 1 1 2 2 2 10 3 3 3 11 4 4 4 100 5 5 5 101 6 6 6 110 7 7 7 111 8 8 10 1000 9 9 11 1001 10 A 12 1010 11 B 13 1011 12 C 14 1100 13 D 15 1101 14 E 16 1110 15 F 17 1111
- 6. 1. B / O / H D (AnAn-1 - - - - A1A0)B (N)10 N = AnBn + An-1Bn-1 + ------ + A2B2 + A1B1 + A0B0 Example (10101)2 ( )10 (1357)8 ( )10 (A2D)16 ( )10 21 751 2605
- 7. 2. D B / O / H (N)10 (AnAn-1 - - - - A1A0)B B N B N1 A0 - - A1 - - - - - - B Nn-1 - An = Nn An-1 Example (55)10 ( )2 (55)10 ( )8 (55)10 ( )16 110111 67 37
- 8. 3. O / H B H / O Example (473)8 ( )2100111011 (An --- A1A0)8 (an3an2an1 --- a13a12a11 a03a02a01)2 (An --- A1A0)16 (an4an3an2an1 --- a14a13a12a11 a04a03a02a01)2 ( )1613B
- 9. TRY YOURSELF ( )16 ( )2 ( )10 11111101 ( )8 FB 253 375 ( )10 ( )8 ( )2 140336 ( )16 49374 1100000011011110 C0DE
- 11. MACHINE LANGUAGE VS ASSEMBLY LANGUAGE