lecture binary and hexadecimal numbers. how machines think computers handle two types of...
Post on 21-Dec-2015
214 views
TRANSCRIPT
![Page 1: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/1.jpg)
LectureBinary and Hexadecimal
Numbers
![Page 2: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/2.jpg)
How Machines Think
• Computers handle two types of information:– Instructions– Data
• The "words" of a machine language are called instructions; each of these gives a command to the CPU
• A computer program (software) is a list of instructions that are executed by the CPU
![Page 3: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/3.jpg)
Off and On
• Computers only recognize off and on, like a light switch
• These switches are represented as binary digits or… bits
• Instructions and data are composed only of a series of bits
![Page 4: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/4.jpg)
Binary Numbers (Bits)
• Bits can be represented as:– 1 or 0– On or Off– Up or Down– Open or Closed– Yes or No– Black or White– Thick or Thin– Long or Short
![Page 5: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/5.jpg)
Bar Codes vs. RFID
• RFID (discuss in Lab 1) Radio Frequency Identification. – Used by Walmart or other retailers to track goods– Has a circuit that can be transmitted to nearby radio
device
• Bar codes cost .005 cents per code• RFID devices cost 7¢ to 30 ¢
per iterm
![Page 6: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/6.jpg)
We count in Base 10 (Decimal)
01234567891011121314959697989910010115161718192021222324Ran out of symbols (0-9), so increment the digit on the left by one unit.
![Page 7: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/7.jpg)
Computers count in Base 2 (Binary)
• Counting in Binary is the same, but with only two symbols– On (1)– Off (0)
0110111001011111000100110101011110011011110111110000110
![Page 8: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/8.jpg)
Converting Binary to Decimal
1 0 1 0 1 1 0 0
1248163264128
00480320128+ + + + + + +
128 + 32 + 8 + 4 = 172
![Page 9: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/9.jpg)
Converting Binary to Decimal
0 1 0 1 0 0 0 11248163264128
1000160640 + + + + + + +
64 + 16 + 1 = 81
![Page 10: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/10.jpg)
Converting Binary to Decimal
- - - -
1248163264128
124016000 + + + + + + +
16 + 4 + 2 + 1 = 23
![Page 11: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/11.jpg)
Converting Binary to Decimal
1248163264128
124016320128+ + + + + + +
128 + 32 + 16 + 4 + 2 + 1 = 183
![Page 12: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/12.jpg)
Bytes
• Eight bits form a single byte– “00110011” is One Byte of Information
• Byte Values:– 00000000 = 0– 11111111 = 255
• As a result, binary numbers almost always written as a full byte (00000001).
![Page 13: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/13.jpg)
Size Matters
Computer memory and storage capacities are represented by their size (megs, gigs, etc)– 1 , 0 = 1 bit– 4 bits = 1 hex character (nibble) – 8 bits = 1 byte – 2^10 = 1,024 bytes or 1 Kilobyte (thousand) – 2^20 = 1,048,576 bytes or 1 Megabyte (million) – 2^30 = 1,073,741,824 or 1 Gigabyte (billion) – 2^40 = 1,099,511,627,776 bytes or
1 Terabyte (trillion)
![Page 14: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/14.jpg)
Future Size Considerations
Thousand, Million, Billion, Trillion, Quadrillion, Quintillian, Hexillion, Heptillion
![Page 15: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/15.jpg)
Binary Influence
• Nintendo 6464 = 01000000
• Color Combinations256 Colors
• Storage1024 MB of RAM (1024 is 256 x 4)
• IP addresses: 255.255.255.255– IP address are comprised of 4 eight-bit numbers– 111111111.11111111.11111111.11111111
![Page 16: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/16.jpg)
Binary to Hexadecimal
• Base 16 instead of Base 2• 16 characters are used instead of 2
• Every Hex character represents 4 bits• 4 bits = 1 nibble (or hex character)• 2 nibbles (2 hex characters) = 1 byte• Easier to get to larger numbers faster
![Page 17: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/17.jpg)
Binary to Hexadecimal
![Page 18: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/18.jpg)
Computers recognize Base 16 (hex)
• Counting in Hex is the same as counting in Bin, but with sixteen symbols
• Still translates to binary
0 1 2 3 4 5 6 7 8 9 A B C D E F
0 = 0000 1 = 0001 2 = 0010 3 = 00114 = 0100 5 = 0101 6 = 0110 7 = 01118 = 1000 9 = 1001 A =1010 B = 1011C = 1100 D=1101 E= 1110 F = 1111
![Page 19: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/19.jpg)
Converting Hex to Bin
![Page 20: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/20.jpg)
Base 16 Hex multiplies by 16 instead of 2 or 10
The hexadecimal system is useful because it can represent every byte (8 bits) as two consecutive hexadecimal digits. It is easier for humans to read hexadecimal numbers than binary numbers.
![Page 21: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/21.jpg)
Let’s Practice Hex! 31
Base 10 = 30 + 1 or 31
Base 2 = 16 + 8 + 4 + 2 + 1 or 1 1 1 1 1
Base 16 = 16 + 15 or 1F (remember only 1 character in hex --- hence we use the letter F to represent the number 15
![Page 22: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/22.jpg)
Let’s Practice Hex! 160
Base 10 = 100+60+0 or 160
Base 2 = 128+0+32+0+0+0+0+0 0r 10100000
Base 16 = 16 x 10 (160) + 0 or A 0 (remember only 1 character in hex --- hence we use the letter A to represent the number 10
Base 10 Decimal 10000000 1000000 100000 10000 1000 100 10 11 6 0
Base 2 Binary 128 64 32 16 8 4 2 11-0 1 0 1 0 0 0 0 0
Base 16 Hex 268435456 16777216 1048576 65536 4096 256 16 10-15 10 0
(15 characters - 0 1 2 3 4 5 6 7 8 9 A=10 B=11 C=12 D=13 E=14 F=15) A 0
Convert
Hex to 8 4 2 1 8 4 2 1Binary 1 0 1 0 0 0 0 0
4-bits = A hex character 4-bits =0 hex character
![Page 23: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/23.jpg)
Let’s Practice Hex! 250
Base 10 = 200+50+0 or 250
Base 2 = 128+64+32+16+8+0+2+0 or 11111010
Base 16 = 16 x 15 = 240 + 1 x 10 = 10 or F A (remember only 1 character in hex --- hence we use the letter F to represent the number 15
Base 10 Decimal 10000000 1000000 100000 10000 1000 100 10 12 5 0
Base 2 Binary 128 64 32 16 8 4 2 11-0 1 1 1 1 1 0 1 0
Base 16 Hex 268435456 16777216 1048576 65536 4096 256 16 10-15 15 10
(15 characters - 0 1 2 3 4 5 6 7 8 9 A=10 B=11 C=12 D=13 E=14 F=15) F A
Convert
Hex to 8 4 2 1 8 4 2 1Binary 1 1 1 1 1 0 1 0
4-bits = F hex character 4-bits = A hex character
![Page 24: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/24.jpg)
Let’s Practice Hex! 179
Base 10 = 100 + 70 + 9 or 179
Base 2 = 128 + 0 + 32 + 16 + 0 + 0 + 2 + 1 or 10110011
Base 16 = 16 x 11 = 176 + 1 x 3 or B 3 (remember only 1 character in hex --- hence we use the letter B to represent the number 11
Base 10 Decimal 10000000 1000000 100000 10000 1000 100 10 11 7 9
Base 2 Binary 128 64 32 16 8 4 2 11-0 1 0 1 1 0 0 1 1
Base 16 Hex 268435456 16777216 1048576 65536 4096 256 16 10-15 11 3
(15 characters - 0 1 2 3 4 5 6 7 8 9 A=10 B=11 C=12 D=13 E=14 F=15) B 3
Convert
Hex to 8 4 2 1 8 4 2 1Binary 1 0 1 1 0 0 1 0
4-bits = B hex character 4-bits = 3 hex character
![Page 25: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/25.jpg)
ASCII (Character Set)
• American Standard Code for Information Interchange
• Provides a means for a byte to represent a number– 0100 0001 (41 Hex) (65 Dec) = A– 0100 0010 (42 Hex) (66 Dec) = B
• Upper-case and lower-case have separate values.
• Numbers and symbols are there too.• Boolean Algebra
![Page 26: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/26.jpg)
ASCII Table
• 1-31 Control Codes• 32-64 Symbols• 65-90 Uppercase• 91-96 More Symbols• 97-122 Lowercase• 123-126 More Symbols• 127 Delete• 128-255 International Symbols
![Page 27: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/27.jpg)
ASCII Table
Link to complete ASCII Chart
![Page 28: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/28.jpg)
Alpha to Hex to Binary nibbles
• C (43)• O (4F)• M
(4D)• P (50)• 2 (32)• 5 (35)
0100 0011 0100 11110100 11010101 00000011 00100011 0101
8 4 2 1 8 4 2 1Alpha Hex
Hex gets there “FASTER” than Binary only for programming code
![Page 29: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/29.jpg)
ASCII Symbols and Characters
• Symbols and characters:– ! – @ – (space)– "
33 or #21 or 0010 000164 or #40 or 0100 000032 or #20 or 0010 000034 or #22 or 0010 0010
Hex Characters convert to binary so each symbol has a binary representation
![Page 30: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/30.jpg)
Other Character Sets
• UTF – Unicode Transformation Formats
• UTF-8; dominant – uses 1-4 bytes to represent characters
• UTF-16• UTF-32
![Page 31: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/31.jpg)
Windows Calculator for Binary
1. Type your number.
2. Choose notation.
3. See new value.
![Page 32: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/32.jpg)
Windows Calculator for Hex
1. Type your number.
2. Choose notation.
3. See new value.
![Page 33: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/33.jpg)
Binary Addition – Rules!
• Remember elementary school– Carry– Double Digits
• New Rules0 0 1 10 1 0 10 1 1 10
![Page 34: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/34.jpg)
Why?
![Page 35: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/35.jpg)
Binary Subtraction – Rules!
• Remember elementary school– Borrow– Double Digits
• New Rules0 1 1 00 1 0 10 0 1 1
1
- - - -
![Page 36: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/36.jpg)
Why?
When you borrow an
“8”
You are getting
two “4s”1 (4)1 (4)
![Page 37: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/37.jpg)
Hex Add & Subtrat
• Remember you are carrying/borrowing
• Note for Subtraction (1/F)
![Page 38: Lecture Binary and Hexadecimal Numbers. How Machines Think Computers handle two types of information: –Instructions –Data The "words" of a machine language](https://reader035.vdocument.in/reader035/viewer/2022062516/56649d555503460f94a31d8a/html5/thumbnails/38.jpg)
There are 10 types of people in the world...
Those who understand binary, and those who
don’t.