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Lab #1 Follow-Up Unix Binary / Hexadecimal Python

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Lab #1 Follow-Up Unix Binary / Hexadecimal Python

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Media Access Control (MAC) address

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B4-D8-A9-00-04-07

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DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F 11×16 + 4×1

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F 11×16 1 + 4×16 0

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F 11×16 + 4×1

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F 11×16 + 4×1 176 + 4

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B 4 DecimalHex(adecimal)0123456789 10A 11B 12C 13D 14E 15F 11×16 + 4×1 176 + 4 180

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All modern numbering systems work this way B 4 11×16 1 + 4×16 0 11×16 + 4×1 176 + 4 180 1×10 2 + 8×10 1 + 0×10 0 100 + 80 + 0 1×100 + 8×10 + 0×1 180

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Why Base 16?

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DecimalHexBinary 000 111 2210 3311 44100 55101 66110 77111 881000 991001 10A1010 11B1011 12C1100 13D1101 14E1110 15F1111

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Why Base 16? DecimalHexBinary 0000000 0110001 0220010 0330011 0440100 0550101 0660110 0770111 0881000 0991001 10A1010 11B1011 12C1100 13D1101 14E1110 15F1111

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B 4 Eight Bits = One Byte DecimalHexBinary 000000 110001 220010 330011 440100 550101 660110 770111 881000 991001 10A1010 11B1011 12C1100 13D1101 14E1110 15F1111 1011 0100

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Why Base Two?

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ENIAC (1946)

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1940s Faster, Cheaper, Smaller 1950s 1960s Today Vacuum tube RelayTransistor Integrated Circuits

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● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = ??? 10 Binary-to-Decimal Conversion

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● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = ??? 10 1 * 2 0 = 1 Binary-to-Decimal Conversion

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● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = ??? 10 1 * 2 0 = 1 +0 * 2 1 = 0

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Binary-to-Decimal Conversion ● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = ??? 10 1 * 2 0 = 1 +0 * 2 1 = 0 +1 * 2 2 = 4

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Binary-to-Decimal Conversion ● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = ??? 10 1 * 2 0 = 1 +0 * 2 1 = 0 +1 * 2 2 = 4 +1 * 2 3 = 8

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Binary-to-Decimal Conversion ● To convert from binary to decimal Start from right Multiply 0,1 by powers of two (1, 2, 4, 8, …) Sum of these products is decimal equivalent ● E.g., 1 1 0 1 2 = 13 10 1 * 2 0 = 1 +0 * 2 1 = 0 +1 * 2 2 = 4 +1 * 2 3 = 8 ____________ 13

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13r 2 = 1 13 ÷ 2 = 6 6r 2 = 0 6 ÷ 2 = 3 3r 2 = 1 3 ÷ 2 = 1 1r 2 = 1 1 ÷ 2 = 0 ___________ 1 1 0 1 Decimal-to-Binary Conversion To convert from decimal to binary 1.Take remainder of decimal number / 2 2.Write down remainder right-to-left 3.If decimal number is zero, we’re done 4.Divide decimal number by 2 5.Go to step 1.

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Fractions 3.25 10 = ???? 2

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Fractions 3. 2 5 3×10 0 + 2×10 -1 + 5×10 -2

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Fractions 3. 2 5 10 = 3×10 0 + 2×10 -1 + 5×10 -2 1 1. 0 1 2 1×2 1 + 1×2 0 + 0×2 -1 + 1×2 -2

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Problem! 3.2 10 = ???? 2

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Google patriot missile failure for a real-world example

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What about text? ASCII: One byte per character

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What about text? Unicode: (Up to) two bytes per character

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Numbers or text? Each application (MS Word, Excel) expects either (ASCII) text or (“raw binary”) numbers Try opening a an Excel spreadsheet in WordPad!

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Computer Number Systems This presentation will show conversions between binary, decimal, and hexadecimal numbers.

Computer Number Systems This presentation will show conversions between binary, decimal, and hexadecimal numbers.

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