Transcript Binary, Hexadecimal, and ASCII PowerPoint Slides

Binary Conversions
Number systems
 Binary to decimal
 Decimal to binary

Binary Humor

There are 10 kinds of people in the world those who understand binary and those
who don't.
Numbering Systems

Base 10 or decimal numbering system
 Base-10
numbering systems dictate that the
numbering scheme begins to repeat after the
tenth digit (in our case, the number 9).
 Zero is always the first number.
 When we count, we usually count "00, 01, 02,
03, 04, 05 , 06, 07, 08, 09, 10, 11, 12, ...“
Numbering Systems

Base 10 or decimal numbering system
 Each
digit to the left and right of the decimal
point is given a name which identifies that
digit's placeholder.
 Each placeholder is a multiple of ten.
 For now lets just consider positive numbers.
Numbering Systems - Base Ten
Each placeholder is a base of
ten.
 10º = ones

Any number to the zero
power is always equal to 1.
 nº=1
 10º=1

10¹ = tens

Any number to the first
power is always equal itself.
 n¹=n
 10¹=10


10² = hundreds
10³ = thousands
T
H
O
U
S
A
N
D
S
7
H
U
N
D
R
E
D
S
T
E
N
S
O
N
E
S
4
0
8
Numbering Systems – Base Ten
Arithmetic expression of 8 in 7408.
 Work right to left of decimal point.
 The ones position in expanded notation
calculating the exponent.

 10º*8=8
is the same as 1*8=8
Numbering Systems – Base Ten
Number
7
4
0
8
Position
Name
Thousands
Hundreds
Tens
Ones
Exponential
Expression
10³*7
10²*4
10¹*0
10º*8
Calculated
Exponent
1000*7
100*4
10*0
1*8
Sum of the powers of ten.
1000*7 + 100*4 + 10*0 + 1*8 = 7408
Numbering Systems – Base two




Binary system is based on multiples of two.
In binary numbering the numbering scheme
repeats after the second digit.
Let's count to five in binary: “0000, 0001, 0010,
0011, 0100, 0101“
Binary numbering includes names for digit
placeholders.
Numbering Systems – Base two

Picture a odometer that is only capable of
counting to two.
Numbering Systems – Base two

Binary placeholders

Decimal placeholders
 Ones
 Ones
 Twos
 Tens
 Fours
 Hundreds
 Eights
 Thousands
 Sixteen's
 Ten-thousands
 Thirty-twos
 Hundred-thousands
 Sixty-fours
 Millions
Numbering Systems – Base two
If the binary system is based on powers of
2, why is there still a "ones" position?
 Remember: Anything to the zero power is
always equal to 1.
 In binary, the "ones" position is
represented by the exponential expression
2º.

Convert Binary to Decimal
Number
1
1
0
1
Position
Name
Eights
Fours
Twos
Ones
Exponential
Expression
2³*1
2²*1
2¹*0
2º*1
Calculated
Exponent
8*1
4*1
2*0
1*1


Sum of the powers of two.
8*1 + 4*1 + 2*0 + 1*1 = 13
Convert Binary to Decimal

Step 1 - Write the binary number in a row,
separating the digits into columns.
Number
1
1
0
1
Convert Binary to Decimal



Step 2 - I want to decide whether each digit placeholder
is "ON" or "OFF.“
"1" is "ON" and a "0" is "OFF.“
We don't have to calculate any digit placeholders that
are turned off.
Number
1
1
0
1
ON/OFF
On
On
Off
ON
Convert Binary to Decimal



Step 3 - Write the exponential expressions ("powers of two") that
represent each placeholder and multiply each expression by 1.
We do this only for the placeholders that are turned ON.
For the placeholders which are turned OFF, we simply bring down
the zero from the number itself
Number
1
1
0
1
ON/OFF
On
On
Off
ON
Exponential
Expression
2³*1
2²*1
0
2º*1
Convert Binary to Decimal

Step 4 - Calculate the exponents to get a simple
multiplication expression for each placeholder.
Number
1
1
0
1
ON/OFF
On
On
Off
ON
Exponential
Expression
2³*1
2²*1
0
2º*1
Calculated
Exponent
8*1
4*1
0
1*1
Convert Binary to Decimal

Step 5 - Solve the multiplication expressions
from step #4.
Number
1
1
0
1
ON/OFF
On
On
Off
ON
Exponential
Expression
2³*1
2²*1
0
2º*1
Calculated
Exponent
8*1
4*1
0
1*1
8
4
0
1
Solved
Multiplication
Convert Binary to Decimal

Step 6 - Add all the multiplication answers from
step #5 together to get our decimal number
Number
1
1
0
1
ON/OFF
On
On
Off
ON
Exponential
Expression
2³*1
2²*1
0
2º*1
Calculated
Exponent
8*1
4*1
0
1*1
8
4
0
1
Solved
Multiplication
Add to
calculate
Value
8+4+0+1=13
Convert Binary to Decimal
Example
Number
1
0
1
1
0
1
ON/OFF
On
Off
On
On
Off
On
Exponential
Expression
25
0
2³
2²
0
2º*1
Calculated
Exponent
32*1
0
8*1
4*1
0
1*1
Solved
Multiplication
32
0
8
4
0
1
Add to
calculate
Value
32+0+8+4+0+1=45
Covert Decimal to Binary


Step 1 - Take the decimal number and divide it
by 2.
Important: NEVER carry your divisions past the
decimal point!
Decimal Number=97
Division
Expression
97/2
Quotient
Remainder
48
1
Covert Decimal to Binary

Step 2 - For each subsequent row, take the quotient from
the previous row and divide it by two
Decimal Number=97
Division Expression
Quotient
Remainder
97/2
48
1
48/2
24
0
24/2
12
0
12/2
6
0
6/2
3
0
3/2
1
1
1/2
0
1
Covert Decimal to Binary
Step 3 – The remainder column only has
ones or zeros.
 The last cell in the remainder column of
the last row must be a "1".
 Read the 1s and 0s in the remainder
column from the bottom to the top, we'll
have our binary number!

Covert Decimal to Binary
Decimal Number=97
Quotient
Remainder
48
24
1
0
24/2
12/2
6/2
12
6
3
0
0
0
3/2
1/2
1
0
1
1
Binary Number=1100001
Direction
Read
Division
Expression
97/2
48/2
Whiteboard Examples In Class
Correction
37
Q
R
37/2
18
1
18/2
9
0
9/2
4
1
4/2
2
0
2/2
1
0
1/2
0
1
0
0
1
0
1
25
24
23
22
21
20
8*0
4*1
2*0
1*1
0
4
0
1
32*1 16*0
Read
DE
1
32
0
32+0+0+4+0+1= 37
The last cell in the remainder column of the last row must be a "1“
because we need to use whole numbers (nonnegative integers).
1 ÷ 2 = 0 because 1 can not be divided into, 1 is the remainder.
36 (Even Number
DE
Q
R
36/2 18
0
18/2
9
0
9/2
4
1
4/2
2
0
2/2
1
0
1/2
0
1
Read
Read
37 (Odd Number)
DE
Q
R
37/2 18
1
18/2
9
0
9/2
4
1
4/2
2
0
2/2
1
0
1/2
0
1
Hexadecimal
Conversation and
ASCII
Hexa + Decimal


Base-16 number system
It’s all Greek to me
 “Sexa”
= Latin = Six
 “Decimal” = Latin = Ten
 In 1963 IBM thought “Sexadecimal” was not politically
correct
 “Hexa” = Greek = Six
 Since the western alphabet contains only ten digits,
hexadecimal uses the letters A-F to represent the
digits ten through fifteen.
Hexadecimal and Computing

It is much easier to work with large
numbers using hexadecimal values than
decimal or binary.
 One
Hexadecimal digit = 4bits
 Two hexadecimal digits = 8 bits
 Eight bits=1 byte
 This makes conversions between
hexadecimal and binary very easy
Counting Hexadecimal

Starting from zero, we count 00, 01,
02,03, 04, 05, 06, 07, 08, 09, 0A, 0B, 0C,
0D, 0E, 0F,10, 11, 12, 13, 14, 15, 16, 17
18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20, 21, 22,
23, 24, 25,....
Decimal
Binary
Hexadecimal
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
10
1010
a
11
1011
b
12
1100
c
13
1101
d
14
1110
e
15
1111
f
Convert Hexadecimal to
Decimal
1
1
A =10
8
163
162
161
160
4096*1
256*1
16*10
8*1
4096
256
160
8
4096+256+160+8= 4520
Convert Decimal to Hexadecimal
4520
Q
R
4520/16
282
(.5*16)=8
282/16
17
(.625*16)=10
10=A
17/16
1
(.0625*16)=1
1/16
0
(.0625*16)=1
11A8



Quotient must be a whole number.
If decimal, multiply decimal portion by 16 for remainder.
Remainder must be a whole number.
Read
DE
Convert Hexadecimal to Binary
Hex


Convert each
hexadecimal digit into
its 4-bit binary
equivalent.
1AB
Bin
1
A
B
0001 1010 1011
000110101011
Convert Binary to Hexadecimal



Converteach 4bit binary
digit into its hexadecimal
equivalent starting from
the right.
If there is an odd number
of bits, add zeros to the
left to make a complete
4bit digit.
110101011
Bin
Hex
0001 1010 1011
1
A
1AB
B
Uses
 Web

pages
http://www.psyclops.com/tools/rgb/
 Networking

MAC address
 Programming

C, C++, C#, Java, Assembly
 Geeky

T-shirts
DEADB4C0FFEE
ASCII







American Standard Code for Information
Interchange
Each character is 7bits + 1bit for parity = 1byte
Represents English characters as numbers, with
each letter assigned a number from 0 to 127
This makes it possible to transfer data from one
computer to another.
Used to store text files
http://www.pcguide.com/res/tablesASCII-c.html
http://nickciske.com/tools/binary.php
Conversion Lab

Section I: Converting from Decimal to Binary
 1)
 2)
 3)
 4)
 5)

11
27
54
113
273
Section II: Converting from Binary to Decimal
 6)
101
 7) 1011
 8) 10100
 9) 111010
 10) 1010001
Conversion Lab


Section III: Convert Hexadecimal to Binary
 11) 43B
 12) DAB
 13) 954
 14) C0FFEE
 15) B0A
Section IV: Convert Binary to Hexadecimal
 16) 11000001111
 17) 10100011110
 18) 100110
 19) 11011110
 20) 101110110001
Conversion Lab


Section V: Convert Hexadecimal to Decimal
 21) FF2
 22) 45
 23) 19D
 24) 345
 25) AA
Section VI: Convert Decimal to Hexadecimal
 26) 27
 27) 85
 28) 562
 29) 4522
 30) 5627