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**Behind the scenes in your computer**

Bits and Bytes Behind the scenes in your computer

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**All computer storage is organized into bytes**

Think of each byte as a little storage bin Each byte is made up of 8 bits Each bit is an electronic circuit that is either on or off (off = 0, on = 1) A specific sequence of 0’s and 1’s in a byte is called a bit pattern

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**So, how many bytes are in your computer?**

Common Prefixes Kilo 103 1,000 Thousand Mega 106 1,000,000 Million Giga 109 1,000,000,000 Billion Tera 1012 1,000,000,000,000 Trillion Typical Capacities: RAM: 1, 2, 4, 6 or 8 GB Diskette: MB Flash drive: 2, 4, 8, 16, 32, 64, 128 GB CD: 800 MB DVD: 4.7 GB Hard Drive: 500 GB – 2 TB

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**Converting Between Units**

To Convert … From To Action KB Bytes Multiply by 1,000 (move decimal point 3 places right) MB Multiply by 1,000,000 (move decimal point 6 places right) GB Multiply by 1,000,000,000 (move decimal point 9 places right) Divide by 1,000 (move decimal point 3 places left) Divide by 1,000,000 (move decimal point 6 places left) Divide by 1,000,000,000 (move decimal point 9 places left) Example 1: KB = ? MB 5200 × 1000 = 5,200,000 bytes 5,200,000 /1,000,000 = 5.2 MB Example 2: 7.5 GB = ? KB 7.5 × 1,000,000,000 = 7,500,000,000 bytes 7,500,000,000 / 1000 = 7,500,000 KB

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You Try: 3.2 MB = ? Bytes 6.4 GB = ? MB 57,000 Bytes = ? KB 25,000 KB = ? MB

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**What kinds of information do you store on your computer?**

numerical values (binary number system) text/character data (ASCII or Unicode) program instructions (machine language) images (jpg, gif, tiff, bmp, wmf, etc.) video (mp4, mov, avi, wmv, etc.) music (mp3, wav, wma, au, etc.)

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**“Kathy Ames” is text It would be stored like this using ASCII codes**

It would be stored like this using ASCII codes

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**Numerical values needed for arithmetic are stored using a different scheme**

The numerical value 40 would be stored like this using the binary number system. (note that “bit” stands for “binary digit”)

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**How do binary numbers work?**

Decimal Number System Binary Number System Base 10 Base 2 10 digits (0,1,2,3,4,5,6,7,8,9) 2 digits (0,1) Positional values based on powers of 10 Positional values based on powers of 2 Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number 8-bit binary number

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**Converting from Binary to Decimal**

What is the decimal value of the bit pattern ? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Simple! Just add up the positional values where the 1’s appear: = 106 So, we say that = 106 decimal

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Simple! Just think about money and consider positional values as bills and 151 “dollars” as the amount we must make. Then “count change” from largest “denomination” to smallest until total value of change is accumulated.

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: 128

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: = 144

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: = 144

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: = 148

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: = 150

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**Converting from Decimal to Binary**

How can we represent the decimal value 151 in binary? Positional Values 128 64 32 16 8 4 2 1 27 26 25 24 23 22 21 20 Binary Number Running Total: = 151 So, 151 decimal =

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**So What is Hexadecimal? (often called “hex”)**

A base 16 number system 16 possible digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Positional values are powers of 16 Mainly used is as “short hand” for binary 1 hex digit = 4 binary digits

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**Hex Digits Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001**

1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111

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**Converting from Hex to Decimal**

What is the decimal value of hex 3B? Positional Values 16 1 161 160 Hex Number 3 B Simple! 3 × 16 + B × 1 = 3 × × 1 = = 59 So, we say that 3B hex = 59 decimal

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**Converting from Hex to Decimal**

What is the decimal value of hex E4? Positional Values 16 1 161 160 Hex Number E 4 Simple! E × × 1 = 14 × × 1 = = 228 So, we say that E4 hex = 228 decimal

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**Let’s take another look at Hex 3B**

Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 So Hex 3B = Binary First Digit Second Digit 3 B 0011 1011 (And note that Binary = = 59 Decimal)

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**Let’s take another look at Hex E4**

Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 So Hex E4 = Binary First Digit Second Digit E 4 1110 0100 (And note that Binary = = 228 Decimal)

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**What about converting Binary 10100010 to Hex?**

Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 First Digit Second Digit 1010 0010

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**What about converting Binary 10100010 to Hex?**

Dec Value 1 2 3 4 5 6 7 Hex Digit 4-bit binary 0000 0001 0010 0011 0100 0101 0110 0111 Dec Value 8 9 10 11 12 13 14 15 Hex Digit A B C D E F 4-bit binary 1000 1001 1010 1011 1100 1101 1110 1111 First Digit Second Digit 1010 0010 A 2 So Binary = A2 Hex

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**Verify that Binary 10100010 and Hex A2 have the same Decimal values**

Binary = = 162 Hex A2 = A × × 1 = 10 × × 1 = = 162

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You try: Convert 210 Decimal to: Binary: Hex: Convert 2D Hex to: Decimal: Convert Binary to:

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Bits & Bytes: How Computers Represent Data

Bits & Bytes: How Computers Represent Data

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