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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 Kilo10 3 1,000Thousand Mega10 6 1,000,000Million Giga10 9 1,000,000,000Billion Tera10 12 1,000,000,000,000Trillion Typical Capacities: RAM: 1, 2, 4, 6 or 8 GB Diskette: 1.44 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 … FromToAction KBBytesMultiply by 1,000 (move decimal point 3 places right) MBBytesMultiply by 1,000,000 (move decimal point 6 places right) GBBytesMultiply by 1,000,000,000 (move decimal point 9 places right) BytesKBDivide by 1,000 (move decimal point 3 places left) BytesMBDivide by 1,000,000 (move decimal point 6 places left) BytesGBDivide by 1,000,000,000 (move decimal point 9 places left) Example 1: 5200 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 01001011 01100001 01110100 01101000 01111001 00100000 00100001 01101101 01100101 01010011 It would be stored like this using ASCII codesASCII 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. 00101000 (note that “bit” stands for “binary digit”)

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How do binary numbers work? Decimal Number SystemBinary Number System Base 10Base 2 10 digits (0,1,2,3,4,5,6,7,8,9)2 digits (0,1) Positional values based on powers of 10Positional values based on powers of 2 Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 8-bit binary number

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Converting from Binary to Decimal Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 01101010 What is the decimal value of the bit pattern 01101010 ? Simple! Just add up the positional values where the 1’s appear: 64 + 32 + 8 + 2 = 106 So, we say that 01101010 2 = 106 decimal

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number How can we represent the decimal value 151 in binary? 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 Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 1 How can we represent the decimal value 151 in binary? Running Total: 128

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 10 How can we represent the decimal value 151 in binary? Running Total: 128

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 100 How can we represent the decimal value 151 in binary? Running Total: 128

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 1001 How can we represent the decimal value 151 in binary? Running Total: 128 + 16 = 144

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 10010 How can we represent the decimal value 151 in binary? Running Total: 128 + 16 = 144

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 100101 How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 = 148

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 1001011 How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 + 2 = 150

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Converting from Decimal to Binary Positional Values 1286432168421 2727 2626 2525 2424 23232 2121 2020 Binary Number 10010111 How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 + 2 + 1 = 151 So, 151 decimal = 10010111 2

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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 01234567 Hex Digit 01234567 4-bit binary 00000001001000110100010101100111 Dec Value 89101112131415 Hex Digit 89ABCDEF 4-bit binary 10001001101010111100110111101111

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Converting from Hex to Decimal Positional Values 161 16 1 16 0 Hex Number 3B What is the decimal value of hex 3B? Simple! 3 × 16 + B × 1 = 3 × 16 + 11 × 1 = 48 + 11 = 59 So, we say that 3B hex = 59 decimal

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Converting from Hex to Decimal Positional Values 161 16 1 16 0 Hex Number E4 What is the decimal value of hex E4? Simple! E × 16 + 4 × 1 = 14 × 16 + 4 × 1 = 224 + 4 = 228 So, we say that E4 hex = 228 decimal

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Let’s take another look at Hex 3B Dec Value 01234567 Hex Digit 01234567 4-bit binary 00000001001000110100010101100111 Dec Value 89101112131415 Hex Digit 89ABCDEF 4-bit binary 10001001101010111100110111101111 First DigitSecond Digit 3B 00111011 So Hex 3B = 00111011 Binary (And note that 00111011 Binary = 32 + 16 + 8 + 2 + 1 = 59 Decimal)

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Let’s take another look at Hex E4 Dec Value 01234567 Hex Digit 01234567 4-bit binary 00000001001000110100010101100111 Dec Value 89101112131415 Hex Digit 89ABCDEF 4-bit binary 10001001101010111100110111101111 First DigitSecond Digit E4 11100100 So Hex E4 = 11100100 Binary (And note that 11100100 Binary = 128 + 64 + 32 + 4 = 228 Decimal)

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What about converting Binary 10100010 to Hex? Dec Value 01234567 Hex Digit 01234567 4-bit binary 00000001001000110100010101100111 Dec Value 89101112131415 Hex Digit 89ABCDEF 4-bit binary 10001001101010111100110111101111 First DigitSecond Digit 10100010

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What about converting Binary 10100010 to Hex? Dec Value 01234567 Hex Digit 01234567 4-bit binary 00000001001000110100010101100111 Dec Value 89101112131415 Hex Digit 89ABCDEF 4-bit binary 10001001101010111100110111101111 First DigitSecond Digit 10100010 A2 So 10100010 Binary = A2 Hex

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Verify that Binary 10100010 and Hex A2 have the same Decimal values Binary 10100010 = 128 + 32 + 2 = 162 Hex A2 = A × 16 + 2 × 1 = 10 × 16 + 2 × 1 = 160 + 2 = 162

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You try: Convert 210 Decimal to: Binary: Hex: Convert 2D Hex to: Binary: Decimal: Convert 10001100 Binary to: Hex: Decimal:

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