The additions simulated by this circuit are
|
0 |
+ |
0 |
+ |
0 |
+ |
0 |
+ |
1 |
+ |
1 |
+ |
1 |
+ |
1 |
+ |
A |
+ |
|
0 |
|
0 |
|
1 |
|
1 |
|
0 |
|
0 |
|
1 |
|
1 |
|
B |
|
|
0 |
|
1 |
|
0 |
|
1 |
|
0 |
|
1 |
|
0 |
|
1 |
|
CIN |
|
|
0 |
|
1 |
|
1 |
|
10 |
|
1 |
|
10 |
|
10 |
|
11 |
|
COUTS |
|
Call the sum and carry outputs from the first half adder Sum1 and Carry1 and Sum2 and Carry2 for the second half adder.
|
A |
B |
CIN |
Carry1 |
Sum1 |
Carry2 |
Sum2 |
COUT |
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
0 |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
|
0 |
1 |
0 |
0 |
1 |
0 |
1 |
0 |
|
0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
|
1 |
0 |
0 |
0 |
1 |
0 |
1 |
0 |
|
1 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
|
1 |
1 |
0 |
1 |
0 |
0 |
0 |
1 |
|
1 |
1 |
1 |
1 |
0 |
0 |
1 |
1 |
Carry1 is worked out from A + B
Sum1 is worked out from A + B
Carry2 is worked out from CIN + Sum1
Sum2 is worked out from CIN + Sum1
COUT is worked out from Carry2 and CIN
We can use a simpler representation of the full adder
And the summary of the truth table is
|
A |
B |
CIN |
|
COUT |
Sum2 |
|
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 |
Compare this with the additions at the top of the page