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1. Digital Logic Structures: Chapter 3. COMP 2610. Dr. James Money COMP 2610. Full Adder. In order to implement a full adder circuit, let’s consider our method for adding binary numbers Recall that this is done in a similar way to long addition for decimal numbers. Full Adder. - PowerPoint PPT Presentation
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Digital Logic Structures: Chapter 3
COMP 2610Dr. James Money
COMP 2610
1
Full Adder
In order to implement a full adder circuit, let’s
consider our method for adding binary
numbers
Recall that this is done in a similar way to
long addition for decimal numbers
Full Adder
Carry: 100110000
110011010
+ 011011100
001110110
Full Adder
Note that for each column of bits, we need
three values:
– Bit from value 1 - ai
– Bit from value 2 - bi
– Carry Bit – carryi
Full Adder
The two outputs of the add are:
– The result of the add is stored in si
– The carry value is stored in carryi+1
When can now formally turn this into a truth
table for adding one bit
Full Adder
ai bi carryi carryi+1 si
0 0 0 0 0
0 0 1 0 1
0 1 0 0 1
0 1 1 1 0
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 1
Full Adder
Full Adder
Figure 3.15 is on the previous slide
PLAs
A Programmable Logic Array (PLA) is a
common building block for building logical
functions
It consists of an array of AND gates, an array
of OR gates, and some way to connect these
outputs
PLAs
PLAs
For a PLA, we consider a truth table with n
inputs and m outputs
You will need 2n AND gates and m OR gates
We then program the connections between
the AND and OR gates
The full adder is an example of this
Logical Completeness
There is an important property to notice before
we leave logic circuits called logical
completeness
We’ve shown that we only need AND, OR,
NOT to form a logic circuit using PLAs
We say {AND, OR, NOT} is logically complete
because of this