Week of November 26

Week of November 26 - Class notes for the week of November...

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Class notes for the week of November 26 th Adders: A B C Sum Cout 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 In class we used the truth tables for the full adder to demonstrate how a truth table can be used to create a logic design. The full adder has three inputs, a bit from number A, a bit from number B, and a carry input (C) from the less significant column. Outputs include a sum bit and a carry bit (Cout): We can write equations for the Cout output using the canonical sum of products technique. For each ‘1’ that appears in the Cout column, we write a AND term and then OR these AND gates together: We can use Boolean logic to simplify this. First we rearrange the order of the terms: then we can collect terms: finally, we simplify and This final version is easily implemented with the parts we have in our lab kit. The Sum output is a little tougher: we factor the first two terms:
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U 1 B 7 4 L S 8 6 A 4 5 6 U 1 C 7 4 L S 8 6 A 9 1 0 8 U 2 A 7 4 L S 0 0 1 2 3 U 2 B 7 4 L S 0 0 4 5 6 U 2 C 7 4 L S 0 0 9 1 0 8 S 1 D S T M 1 S 1 D S T M 2 S 1 D S T M 3 C i n B A S u m C o u t and simplify: now we factor the right two terms: and recognize the XNOR simplification: and another XOR simplification: Thi s is an especially tidy outcome since the B XOR C term is shared with the Cout expression. In circuit terms, this means that we can share circuitry as shown below.
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Week of November 26 - Class notes for the week of November...

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