Transcript Computer Arithmetic--Binary, Octal, Hexadecimal

ID 2950
Technology and the Young Child
Computer Arithmetic:
Binary, Octal and Hexadecimal
Presented by
Frank H. Osborne, Ph. D.
© 2005
Bits and Bytes
• A bit is a binary digit.
• A bit is like a light switch. It has two
positions, off = 0 and on = 1.
Bits and Bytes
• A byte is like a row of 8 switches.
Bits and Bytes
• Because it has only two digits, 0 and 1,
the binary number system is base 2.
• We are accustomed to using base 10
which has 10 digits which are as follows:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Computers work in base 2 while we work
in base 10.
Review of Base 10
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Consider the number 3178.
3 is the thousands place = 3000 = 3 x 103
1 is the hundreds place = 100 = 1 x 102
7 is the tens place = 70 = 7 x 101
8 is the units place = 8 = 8 x 100
Review of Base 10
• Each numeral is multiplied by 10 raised
to the appropriate power for its position.
Review of Base 2
• A byte is 8 bits which are like 8 switches.
Properties of Base 2
• Each numeral is multiplied by 2 raised to
the appropriate power for its position.
• So, a byte can hold a number between 0
and 255.
Converting Base 2 Numbers to Base 10
• What is the value of 0100 1001 in base 10?
• The answer is 73.
• To solve this type of question, remember the
sequence of positions.
• The values are in the following sequence:
1, 2, 4, 8, 16, 32, 64, 128
• Find which switches are on and add the
values together.
Octal is Base 8
• If we take the bits by threes,
we get octal, which is base 8.
• The base 8 numerals are:
0, 1, 2, 3, 4, 5, 6, 7
The positions for the octal digits are:
000 = 0 100 = 4
001 = 1 101 = 5
010 = 2 110 = 6
011 = 3 111 = 7
Use of Octal
• Some computers actually use octal for
calculations but it is a big problem because
the 8-bit byte is not evenly divisible by 3.
• Octal us used for setting the UNIX access
rights to directories on server computers.
• You will use this for sure if you are putting
things into a directory on a server for use on
the Internet.
Setting UNIX Access Rights
• UNIX access rights are assigned to every file
and directory on the server.
• Rights have the form: drwxrwxrwx
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d means if it is a directory or not
r means read
w means write
x means execute
• There are three sets of rwx rights. These are
for you, for those in your group and for
everyone else. Each letter is one bit.
Setting UNIX Access Rights
• On the Kean turbo server, a faculty member
may have an account.
• All other faculty are in the same group.
• Anyone from the outside, such as on the
World Wide Web, can have access if the
rights are set correctly.
Setting UNIX Access Rights
• drwxrwxrwx - The first set of bits is for
yourself. You want to be able to read, write,
create, delete or alter your file without any
problems. Use octal 7 = 111 to set this part.
• drwxrwxrwx - This is for your group--the
other users at your place. Unless you want
someone monkeying with your files, let them
have read-only (100 = 4) which makes it r--.
If you do not want them to know it is there,
set it to 000 = 0, which makes it ---.
Setting UNIX Access Rights
• drwxrwxrwx - The last set of bits is for
everybody else.
• For your Internet pages, make a directory
called www and set the access rights to 100
which makes it read-only. The server will let
anyone on the Internet read the contents,
but they will not be able to delete or change
anything.
• So, your www directory is set as 447 which
corresponds to dr--r--rwx.
Hexadecimal is Base 16
• If we take the bits by fours, we get
hexadecimal, which is base 16.
• The base 16 numerals are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
• As base 10 does not have single numerals
for the numbers from 10-15 we use A-F.
Table of Binary and Hex Equivalents
Properties of Hexadecimal
• A hexadecimal number is exactly one-half
of a byte.
• Since a byte can be from 0-255 in
decimal, it also can be from #00 to #FF in
hexadecimal.
• Use the pound sign (#) as a prefix for
hexadecimal numbers.
• Binary and hexadecimal numbers carry
to the other half of the same byte at the
same time.
Uses of Hexadecimal
• On the Internet, documents are written
in HTML, the hypertext markup
language.
• All colors on computers are a
combination of three colors; red, blue
and green; known as RGB.
• In HTML, you set the values of RGB
using hexadecimal numbers.
• The form for a color is: #RRGGBB
Some Hexadecimal HTML Color Codes
More about Hexadecimal Color Codes
• With #RRGGBB, each can have a value
from 0 to 255. This gives:
256 x 256 x 256 = 16, 777, 216 different
possible colors.
• The most commonly used hex values are:
#00, #33, #66, #99, #CC, and #FF. These
give a total of 216 colors.
• Find Dave Taylor's list at the following url:
www.intuitive.com/coolsites/colors.html
ASCII Codes
• ASCII stands for American Standard Code
for Information Interchange.
• ASCII values range from 0 to 255.
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Values 0 through 31 - control characters
32 through 47 are special keyboard characters
48 through 64 are numerals and characters
65 through 96 capital letters and characters
97 through 127 lower case letters and
characters
– 128 through 255 special characters
The End