**Home** / **converting a number to binary** / DECIMAL, BINARY, AND HEXADECIMAL - University of …

DECIMAL, BINARY, AND

HEXADECIMAL

Decimal Numbering System

Ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Represent larger numbers as a sequence of digits

? Each digit is one of the available symbols

Example: 7061 in decimal (base 10)

? 706110 = (7 x 103) + (0 x 102) + (6 x 101) + (1 x 100)

Octal Numbering System

Eight symbols: : 0, 1, 2, 3, 4, 5, 6, 7

? Notice that we no longer use 8 or 9

Base Comparison:

Base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12...

Base 8: 0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14...

Example: What is 158 in base 10?

? 158 = (1 x 81) + (5 x 80) = 1310

Example: What is 70618 in base 10?

? 70618 = (7 x 83) + (0 x 82) + (6 x 81) + (1 x 80) = 363310

How do you change numbers to binary? To convert a decimal number to binary floating point representation: Convert the absolute value of the decimal number to a binary integer plus a binary fraction. Normalize the number in binary scientific notation to obtain m and e. Set s=0 for a positive number and s=1 for a negative number.

Title: Microsoft PowerPoint - CSE351-L02-binary_16au.pptx

Author: justi

Creator: PScript5.dll Version 5.2.2

Producer: Acrobat Distiller 15.0 (Windows)

CreationDate: Fri Sep 30 22:48:07 2016

ModDate: Fri Sep 30 22:48:07 2016

Tagged: no

Form: none

Pages: 21

Encrypted: no

Page size: 612 x 792 pts (letter) (rotated 90 degrees)

File size: 198557 bytes

Optimized: yes

PDF version: 1.5