TongLecture3

TongLecture3 - CS281 Lecture Notes 3 Tuanjie Tong Review:...

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CS281 Lecture Notes 3 Tuanjie Tong
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Review: Complement notation. Decimal 2’s complement Sign-Magnitude -8 1000 -- -7 1001 1111 -6 1010 1110 -5 1011 1101 -4 1100 1100 -3 1101 1011 -2 1110 1010 -1 1111 1001 0 0000 1000/0000 1 0001 0001 2 0010 0010 3 0011 0011 4 0100 0100 5 0101 0101 6 0110 0110 7 0111 0111
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Summary So far … Binary arithmetic Addition, subtraction, multiplication etc. Next … Designing digital circuits that implement binary arithmetic. Understand boolean algebra Use boolean algebra equations to design digital circuits.
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Why study algebra Consider this problem: There are a flock and some shepherds. If you count all the heads, you get 30; if you count all the legs, you get 100. So how many sheep and how many shepherds are there? Easier to solve using algebra. For similar reasons, digital systems are easier to design using boolean algebra.
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Getting our terms correct Boolean algebra Handling Boolean equations. Boolean equations Also known as boolean expressions Also known as binary equations/expressions (though not very precise).
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Key components of a digital circuit Digital devices use binary numbers for computations. At a high level, you can think of them as devices that:
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TongLecture3 - CS281 Lecture Notes 3 Tuanjie Tong Review:...

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