Discussion in 'General Electronics Chat' started by samhor, Apr 20, 2009.

1. ### samhor Thread Starter New Member

Apr 20, 2009
2
0
Can some one help me with the truth table for the half adder.

I have found it on this site : http://isweb.redwoods.cc.ca.us/INSTRUCT/CalderwoodD/diglogic/half-add.htm

but i would like a sum up on it.

For example :

NOT GATE

INPUT A | INPUT B
0 1
1 0

So you could say that the output is the opposite to the input.

Can you think of some similar for the half adder.

2. ### kamall2050 New Member

Apr 20, 2009
5
0
I gone thruogh the website.Can you tell me where you get confused

Last edited: Apr 20, 2009
3. ### Papabravo Expert

Feb 24, 2006
11,946
2,560
Sure, a half adder is a combinatorial circuit that takes two boolean inputs and produces two boolean outputs. The inputs are often called A and B and represent bits of a larger number. The outputs are called Sum and Carry. Further the Sum is the exclusive OR of A and B, while the logical AND of A and B. A half adder can only be used in the first stage of a multibit adder because every other stage requires a carry INPUT.

So a Full Adder is a combinatorial circuit with three inputs: A, B, and Carry In. The Full Adder has two outputs: Sum and Carry Out.

Is that the summary you were looking for?

4. ### samhor Thread Starter New Member

Apr 20, 2009
2
0
i need to make a rule like i did for
NOT GATE

INPUT A | INPUT B
0 1
1 0

So you could say that the output is the opposite to the input.

I need one for the half adder. Truth table is on the link

5. ### steinar96 Active Member

Apr 18, 2009
239
4
You are looking for a simple rule for the half adder but there is none as simple as you made for the NOT gate.

If you understand the boolean logic behind the half adder you shouldnt need a rule either since it's actually pretty trivial to understand boolean wise.

I would advice you to learn basic boolean math. That way you dont need to remember rules for every digital circuit equation you see (pretty much impossible).

If we look at the half adder circuit on the website you linked you should see that the outputs are governed by the equations

S = A XOR B;
C = A AND B;

The AND is multiplication in binary and is pretty trivial and is just like decimal math while we're only talking about 1 digit binary numbers. That is

0*0 = 0;
0*1 = 0;
1*0 = 0;
1*1 = 1;

The XOR gate is a little more complicated but in boolean algebra the XOR operator is defined as.

A XOR B = A'B + AB'. The ' is the complement sign and is equal to NOT. AB means the 2 numbers and multiplied together.

A' = NOT A. So if A = 0 then A' = 1 and vice versa.

The truth table for the half adder is: (A and B inputs, S = sum, C = carry)

A B S C
0 0 0 0
1 0 1 0
0 1 1 0
1 1 0 1

If we look at the governing circuit equations you'll see that the values for S and C match the values the equations give for values A and B.

If A = B = 0. We have S = 01 + 10. Since any number multiplied by zero is zero the equation gives us zero which is also the number in the truth table. The boolean operation X + Y (X and Y are binary numbers) only gives us zero as long as X and Y are both zero which is the case. Otherwise it's 1.

It's obvious that C = 0*0 = 0.

Second entry (A = 1, B = 0) gives us
S = 01 + 11 = 0 + 1 = 1;
C = 0*1 = 0;

If we have A = B = 1 on the other hand which is the last case in the truth table the equations give us.
S = 10 + 01 = 0 + 0 = 0;
C = 1*1 = 1.

As you see there is a bit of math behind the truth table, but the math is very simple once you get used to manipulating binary numbers and once you are familiar with the basic set of boolean operators.

Last edited: Apr 20, 2009
6. ### Papabravo Expert

Feb 24, 2006
11,946
2,560
Am I crazy or did I not say:
1. Sum = A .XOR. B
2. Carry = A .AND. B
Are you teliing me you can't write down a truth table from those two statements?

7. ### kakin New Member

Mar 24, 2009
9
0
steinar already gave a full explanation. In simple terms you need two "rules", one for each output

a xor b for sum: if either input, but not both, is 1, sum is 1, 0 otherwise
a and b for carry: if both inputs are 1, carry is 1, 0 otherwise

8. ### logysys New Member

Jul 9, 2006
2
0
Hi
For Half adder , we can say that the sum is the x-or of all inputs.

9. ### laughing_gas New Member

Apr 25, 2009
5
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ther's no other way really to sum it up.. it's governed by the boolean algebra rules. there's nothing really complicated by those truth tables when you know the very basic of boolean algebra.