About half adders

First, we are starting with a simple half adder circuit
from the school books.

It uses a 7408 AND gate, and a 7486 XOR gate.

Q = A + B, and the (high active) carry output
turns to 1, if A = 1 and B = 1.

If you only happen to have 7400 NAND gates,
there is another approach which is mentioned
less often in those school books:

Downside is, that the carry output of this schematic
is low active, means that A = 1 and B = 1 turns the
carry output to 0.

For building a full adder, we need two half adders:

The 7400 NAND approach:

Note, that if you take a NAND gate and invert both
intput, it turns into an OR gate.
And that's why the carry output of this full adder
is high active.

"Why is that guy warming up old boring basics again ?",
You may ask now.

Ok, to make things a bit more difficult to understand,
we now build a half adder with 7410 three_input NANDs:

Note the blue marked control signals T, X, Y and S.

Then stare for a while at this picture above,
think about the implications,
and then go for the next page of this article.

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