116 lines
2.6 KiB
Markdown
116 lines
2.6 KiB
Markdown
# lec9
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This lecture has a corresponding activity found in `lab/` it is called `combinational-logic.md`.
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It is more useful to practice combinational logic as opposed to read about it so the sub section here will be minimal in information.
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It's recommended that you try as many of the problems in the activity until you understand the concept, _don't bother doing them all_.
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## Combinational Logic
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### OR
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`a+b` is equivalent to saying `a` or `b`.
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### AND
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`ab` is equivalent to saying `a` and `b`.
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Note that this syntax is simlar to multiplication so `a*b` is equivalent to the above.
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### NOT
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`!a` is equivalent to saying not `a`.
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We can also denote it with a bar over the expression we want to _not_.
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### Big AND
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Behavior is the same as an `and` but instead of two inputs we can have many more inputs.
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It will only ever return a 1 if all inputs are 1.
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### Big OR
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Again we are mimicing the behvior of the normal or gate but this time we can have multiple inputs as opposed to just two.
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If only one of the many inputs is 1 then we return a 1 for the output of the Big OR.
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## Decoders
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Here we'll learn by doing
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```
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Selector = 2 Bits
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Output = 4 Bits
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```
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As a challenge you can try using the combinational logic gates from above to try and tackle this yourself
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|s1 |s2 |o3 |o2 |o1 |o0 |
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|---|---|---|---|---|---|
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| 0 | 0 | 0 | 0 | 0 | 1 |
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| 0 | 1 | 0 | 0 | 1 | 0 |
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| 1 | 0 | 0 | 1 | 0 | 0 |
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| 1 | 1 | 1 | 0 | 0 | 0 |
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## Multiplexor
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Typically we'll refer to multiplexors by their size.
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> what does it do?
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It takes a signal as `2^n` inputs and out puts out `n` signals as output.
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Example: We have a selector(s0), two inputs[in0 & in1], and one output `out`.
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The selector will select an input and we will generate some output in `out`.
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|s0 | i1 | i0 | out|
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|---|---|---|---|
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|0 | 0 | 0 | 0|
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|0 | 0 | 1 | 1|
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|0 | 1 | 0 | 0|
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|0 | 1 | 1 | 1|
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|1 | 0 | 0 | 0|
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|1 | 0 | 1 | 0|
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|1 | 1 | 0 | 1|
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|1 | 1 | 1 | 1|
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This ultimately lets us pick data out of memory given some address.
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## Half Adder
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For now we'll take two inputs and get 1 output, with a carry-output.
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Let's add 2 bits
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|a|b|out|
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|0|0|0|
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|0|1|1|
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|1|0|1|
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|1|1|0|
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What about the carry bit however? What would _it_ look like given the preivous operations?
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|a|b |carryout|
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|0|0 |0|
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|0|1 |0|
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|1|0 |0|
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|1|1 |1|
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Before what this implies note that the result of the carryout resembles
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## Full Adder
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Two inputs, One output, One carry-out, One carry-in
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Here we'll add up `a & b`(inputs) and `c` carry-in
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|c|a|b |output|
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|0|0|0 |0|
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|0|0|1 |1|
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|0|1|0 |1|
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|0|1|1 |0|
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|1|0|0 |1|
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|1|0|1 |0|
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|1|1|0 |0|
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|1|1|1 |1|
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