# A question in building a circuit using 2 full adders

#### transgalactic

which produces a sum of 2 bit numbers x0x1 y0y1
the output is C (carry)
S0S1

the problem is i know how to build a truth table and a KARNO table
and even how to build this circuit

i know how to build a full adder circuit

the problem is i dont know how to build this task using 2 full adders

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#### berkeman

Mentor
What does the truth table of a 2x 2-bit full adder look like?

#### transgalactic

there is no 2 on two full adder
there is only a 1 on 1 plus carry in adder (AKA full adder)

i showed the formula of the sum and the carry out in the drawing

http://img160.imageshack.us/my.php?image=img86211bi8.jpg

what now??
i dont know how to use this basic component in order to solve this
question

as i say again
there is no problem for me to build a truth table for all the
possibilities and to make a KARNO table out of it
and then to build a circuit

????????????????

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#### Phrak

A full adder has three inputs and two outputs. Can you name them?

#### transgalactic

i showed it all in the drawing
there is the input carrier
the firstbit
the secondbit
the output sum
the output carrier

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#### Phrak

Hi, Trans. This sounds like a homework question, so i'm following berkeman's lead in attempting to lead you to an answer, rather than giving it away.

Binary addition is just like adding up decimal numbers longhand. It might help if you tried some examples. Like adding 0110 to 1011. It's binary so the carry-out only has one of two value-- zero or one. The carry out of the one's place is carried into the two's place. The carry out of the two's place is carried into the four's place, and so on.

#### transgalactic

ye i understand that i can even show you the sketch in the book that explains that
http://img356.imageshack.us/my.php?image=img86221gg8.jpg

so like this story of herztel and gretel
where is the next bread peace???
cause i still dont have any idea of how to subtitute 2 adders in the circuit
that i am supposed to build

what is the next step in leading me for understanding this question??

#### Phrak

You can really think of all this as the same as adding columns of normal, base 10 numbers. Except that your doing base 2. Check it out.

_999
+200
-----
1199

There's no carry into the ones place. Thats that same as having the carry into the one's place a zero. So you tie the first carry-input to ground.

The last stage in the example is the hundreds-place. Its carry-out goes straight to the answer. It's the thousands-place digit.

When they do this in an 8 bit CPU you can add up two 8 bit numbers and get a result that needs to fit in 9 bits. So they leave the last carry out in a special bit register, appropriately called the 'carry', so that you can still use it. It can become the carry-input for the next 8 bit addition you do. This allows you to add 16, 24, and 32 bit numbers 8 bits at a time.

The biggest number you can add with two stages is 11 binary to 11 binary.

_11
+11
---
110

Some thing as base 10. You have two 2-bit numbers coming in. But you get a three bit number coming out.

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#### transgalactic

so i understood that my last carry is the next bit place
and that isntead of putting the first carry in sign 0
i should have put a ground there.

except that
my solution is ok?

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#### Phrak

So your "Cout" could be called S2. Bit zero's carry-in is a zero if your doing it on paper. If you're building it in hardware with positive logic you tie it low or tie it to ground.

I that should do it.

thanks

good luck

#### Danger

Gold Member

Sorry... I'm having a slow day at work and had to chirp up. Carry on.

#### rbj

which produces a sum of 2 bit numbers x0x1 y0y1
the output is C (carry)
S0S1

the problem is i know how to build a truth table and a KARNO table
and even how to build this circuit

i know how to build a full adder circuit

the problem is i dont know how to build this task using 2 full adders
think about what you do when you add two binary numbers. which bits do you start with? what bits' results depend on what happens at the other bits?

i'm surprized it isn't depicted in your text book.

#### transgalactic

ok i think i got the consept
do you have anything to say about my solution

is it ok by you??

#### transgalactic

i think that i depicted every thing
i got the input bits
i got the output bits
i got the carry out bit
which should have been the next bit in line on the third place

what did i missed??

#### rbj

listen, what you have on your jpg are ad hoc notes about the operation of a single bit in the adder. what you need to do is think about how you would string together two of these single bit adders into a two bit adder.

#### transgalactic

i dont know what is a two bit adder
for me a have the basic operation of full adder
to do that

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#### rbj

a single full adder adds one bit (the "nth bit") from two binary numbers together with the Carry In bit (so the sum of these 3 bits can be 0, 1, 2, or 3 or 00, 01, 10, or 11 in binary). the result is the two bits i shown to the left. the left bit is the Carry Out bit and the right bit is the nth bit of the sum.

what do you do with the Carry Out the nth bit of a full adder?

"A question in building a circuit using 2 full adders"

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