IST4_lec6

IST4_lec6 - IST 4 Information and Logic IST 4: Planned...

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IST 4 Information and Logic
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mon tue wed thr fri 31 M1 1 7 M1 14 2 1 21 3 2 28 3 5 4 12 5 4 19 26 6 5 2 6 IST 4: Planned Schedule – Spring 2008 x= hw#x out x= hw#x due = today T Mx= MQx out Mx= MQx due midterms midterms T
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I hope you started??
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The Babylonians knew everything…. It is all about SYNTAX… Leibniz was the founder of information science…. IST 4 is focusing on CONTEXT…
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I V X L C D V M 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 0 2 2 3 4 5 6 7 8 9 0 1 3 3 4 5 6 7 8 9 0 1 2 4 4 5 6 7 8 9 0 1 2 3 5 5 6 7 8 9 0 1 2 3 4 6 6 7 8 9 0 1 2 3 4 5 7 7 8 9 0 1 2 3 4 5 6 8 8 9 0 1 2 3 4 5 6 7 9 9 0 1 2 3 4 5 6 7 8 Algorithm = a procedure for syntax manipulation Gottfried Leibniz 1646-1716 Use the smallest syntax possible Binary – 0 and 1
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Algorithms – Syntax Manipulation 0 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 0 2 2 3 4 5 6 7 8 9 0 1 3 3 4 5 6 7 8 9 0 1 2 4 4 5 6 7 8 9 0 1 2 3 5 5 6 7 8 9 0 1 2 3 4 6 6 7 8 9 0 1 2 3 4 5 7 7 8 9 0 1 2 3 4 5 6 8 8 9 0 1 2 3 4 5 6 7 9 9 0 1 2 3 4 5 6 7 8 1 9 0 1 2 3 4 5 6 7 8 0 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 1 3 0 0 0 0 0 0 0 1 1 1 4 0 0 0 0 0 0 1 1 1 1 5 0 0 0 0 0 1 1 1 1 1 6 0 0 0 0 1 1 1 1 1 1 7 0 0 0 1 1 1 1 1 1 1 8 0 0 1 1 1 1 1 1 1 1 9 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 2 symbol adder c s d1 d2 c
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Algorithms – Syntax Manipulation 2 symbol adder c s d1 d2 c 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 sum carry
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Algorithms – Syntax Manipulation 2 symbol adder 1 0 1 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder c c 1 1 c 2 symbol adder c c 1 0 c 2 symbol adder c c 0 0 c 2 symbol adder c c 1 1 0 1101 + 1001 = ??
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder c c 1 1 c 2 symbol adder c c 1 0 c 2 symbol adder c c 0 0 c 2 symbol adder 1 0 1 1 0 1101 + 1001 = ??
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder c c 1 1 c 2 symbol adder c c 1 0 c 2 symbol adder 0 1 0 0 1 2 symbol adder 1 0 1 1 0 1101 + 1001 = ??
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder c c 1 1 c 2 symbol adder 0 1 1 0 0 2 symbol adder 0 1 0 0 1 2 symbol adder 1 0 1 1 0 1101 + 1001 = ??
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder 1 0 1 1 0 2 symbol adder 0 1 1 0 0 2 symbol adder 0 1 0 0 1 2 symbol adder 1 0 1 1 0 1101 + 1001 = ??
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0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 2 symbol adder 1 0 1 1 0 2 symbol adder 0 1 1 0 0 2 symbol adder 0 1 0 0 1 2 symbol adder 1 0 1 1 0 1101 + 1001 = 10110 13 + 9 = 22 We used 4 adders to add two 4 bit numbers
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Algorithms – Syntax Manipulation 2 symbol adder c s d1 d2 0 We demonstrated addition of two binary numbers 0 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 Multiple addition? 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 ?? ??
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Algorithms – Syntax Manipulation 2 symbol adder c s d1 d2 0 Q: Can you add three 4-bit numbers with eight 2-symbol adders? 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 0 Multiple addition Q: If yes, how? We used 4 adders to add two 4 bit numbers ist
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Key Questions Related to Boxes Composition: How to build big s-boxes from small s-boxes? Building blocks: What are ‘good’ small s-boxes? Efficiency: How to build big s-boxes from small s-boxes while reducing cost and increasing performance ?
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IST4_lec6 - IST 4 Information and Logic IST 4: Planned...

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