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CS 230 Introduction to Computers and Computer Systems Lecture 1 Number Representation CS 230 - Spring 2020 1-1 Number Representation Radix representation radix also know as base Writing natural numbers using a finite alphabet

  1. CS 230 – Introduction to Computers and Computer Systems Lecture 1 – Number Representation CS 230 - Spring 2020 1-1

  2. Number Representation  Radix representation  radix also know as base  Writing natural numbers using a finite alphabet  Given an n-digit number in base r d n − 1 d n − 2 d n − 3 ... d 3 d 2 d 1 d 0  Integer value is CS 230 - Spring 2020 1-2

  3. Radix Representation  Humans: base-10, decimal  why?  Computers: base-2, binary  why? electrical simplicity  analog/digital conversion (high vs. low voltage)  low-level decimal conversion?  storage expansion / waste CS 230 - Spring 2020 1-3

  4. Examples Decimal: 135 10 5x10 0 + 3x10 1 + 1x10 2 = 135 10 Binary: 10011 2 1x2 0 + 1x2 1 + 0x2 2 + 0x2 3 + 1x2 4 = 19 10 Hexadecimal: A32 16 2x16 0 + 3x16 1 + 10x16 2 = 2610 10 Septenary: 1440 7 0x7 0 + 4x7 1 + 4x7 2 + 1x7 3 = 567 10 Use letters starting with A to express digits > 9 CS 230 - Spring 2020 1-4

  5. Conversion from Decimal  Repeatedly divide by target base  Remainders generate digits  from right to left CS 230 - Spring 2020 1-5

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