principleMinor
Full Adder vs. Half Adder
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fullhalfadder
Problem
I'm having some trouble figuring out where the "Carry in" value comes from in respects to a one bit full adder diagram. I understand the below half adder,
but my question is: is the the output of the bottom-most AND gate in the bottom diagram equal to the output "C" in the top diagram (Assuming A and B are constant throughout) - Is Cin from the bottom diagram equal to C in the top diagram?
but my question is: is the the output of the bottom-most AND gate in the bottom diagram equal to the output "C" in the top diagram (Assuming A and B are constant throughout) - Is Cin from the bottom diagram equal to C in the top diagram?
Solution
The C's are not the same, but your statement about the AND gate is right.
Unfortunately, the people who drew your full-adder decided to save space instead of maximizing readability. This image does a better job of showing the relationship between half adders and full adders, even though the circuit is identical to the one above:
If they'd just put the wire splitting points inside the grey boxes showing the half-adders instead of outside, they'd be perfect.
Here's a block diagram you can use to see the exact relationship between a half-adder and an adder. It shows clearly something I find quite interesting about adders. The 'or' at the end looks like it could swallow a carry if both half adders were to emit a carry bit at the same time. It seems like we might need another half adder to resolve this, in a never ending chain. However, if you run the truth tables for the half-adder, you find that it is impossible for both half-adders to carry at the same time. Rejoice!
Unfortunately, the people who drew your full-adder decided to save space instead of maximizing readability. This image does a better job of showing the relationship between half adders and full adders, even though the circuit is identical to the one above:
If they'd just put the wire splitting points inside the grey boxes showing the half-adders instead of outside, they'd be perfect.
Here's a block diagram you can use to see the exact relationship between a half-adder and an adder. It shows clearly something I find quite interesting about adders. The 'or' at the end looks like it could swallow a carry if both half adders were to emit a carry bit at the same time. It seems like we might need another half adder to resolve this, in a never ending chain. However, if you run the truth tables for the half-adder, you find that it is impossible for both half-adders to carry at the same time. Rejoice!
Context
StackExchange Computer Science Q#51255, answer score: 8
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