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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
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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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View Full DocumentU 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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 Fall '07
 Westerfield

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