Lecture 1 Number Representation CS 230 - Spring 2020 1-1 Number - - PowerPoint PPT Presentation

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Lecture 1 Number Representation CS 230 - Spring 2020 1-1 Number - - PowerPoint PPT Presentation

Jan 16, 2023 249 likes •976 views

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

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CS 230 – Introduction to Computers and Computer Systems Lecture 1 – Number Representation

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Number Representation

 Radix representation

 radix also know as base

 Writing natural numbers using a finite alphabet  Given an n-digit number in base r  Integer value is

dn− 1dn− 2dn− 3...d3d2d1d0

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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

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Examples

Decimal: 13510 Binary: 100112 Hexadecimal: A3216 Septenary: 14407

Use letters starting with A to express digits > 9

5x100 + 3x101 + 1x102 = 13510 1x20 + 1x21 + 0x22 + 0x23 + 1x24 = 1910 2x160 + 3x161 + 10x162 = 261010 0x70 + 4x71 + 4x72 + 1x73 = 56710

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Conversion from Decimal

 Repeatedly divide by target base  Remainders generate digits

 from right to left

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