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Question 8.6: Implement a full adder circuit using a 3-to-8 line decoder.

Implement a full adder circuit using a 3-to-8 line decoder.

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A decoder with an OR gate at the output can be used to implement the given Boolean function. The decoder should at least have as many input lines as the number of variables in the Boolean function to be implemented. The truth table of the full adder is given in Table 8.11, and Fig. 8.22 shows the hardware implementation.

From the truth table, Boolean functions for SUM and CARRY outputs are given by the following
equations:

Sum output S=\sum{1,2,4,7}                 (8.8)

Carry output C_{0}=\sum{3,5,6,7}                  (8.9)

Table 8.11 Example 8.6.
C_0 S C B A
0 0 0 0 0
0 1 1 0 0
0 1 0 1 0
1 0 1 1 0
0 1 0 0 1
1 0 1 0 1
1 0 0 1 1
1 1 1 1 1
8.61

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