Half Adder Circuit – The way it Works

A Half Adder is a digital circuit that provides binary numbers. On this tutorial, you’ll be taught the way it works, its fact desk, and the right way to implement one utilizing logic gates. 

Half Adder Circuit
A Half Adder Circuit

What’s a Half Adder?

A Half Adder is a digital circuit that carries out the addition of binary numbers. It’s the only of digital adders and you’ll construct one utilizing solely two logic gates; an XOR gate and an AND gate.

The Half Adder can add solely two 1-bit numbers. The distinction between a Half Adder and a Full Adder is that the primary one doesn’t have a Carry enter.

All of the attainable mixtures of 1-bit binary additions are proven under:

All the possible combinations of 1-bit binary additions

You want two bits to symbolize the outcome for the reason that highest attainable results of including two 1-bit numbers is 2 (“10” in binary).

You’ll be able to add this right into a fact desk utilizing the 4 attainable mixtures of 1-bit binary additions given earlier than. The adder takes two inputs, A and B, and generates two outputs, one for the Sum (S) and one other for the Carry (C). So the reality desk turns into:

Enter A Enter B Output S Output C
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
Half Adder Fact Desk

How does the Half Adder work?

To grasp the right way to create a Half Adder circuit you should utilize its fact desk. The very first thing you’ll want to do is separate the S output and construct its personal fact desk.

Enter A Enter B Output S
0 0 0
0 1 1
1 0 1
1 1 0
Sum (S) output Fact Desk

If you understand your logic gates, you may discover that this seems precisely like the reality desk of an XOR gate. And also you’re proper. So to implement the Sum (S) output, you’ll want an XOR gate:

XOR gate for S output

Subsequent, it’s time to deal with the C output:

Enter A Enter B Output C
0 0 0
0 1 0
1 0 0
1 1 1
Carry (C) output Fact Desk

For those who look at it rigorously, you’ll see that it behaves the identical as an AND gate because it solely returns one when each inputs are one. Which means to create the C output you should utilize an AND gate:

AND gate for C output

Lastly, you possibly can mix the circuits for producing the S and C outputs to construct the entire Half Adder circuit diagram:

Combining the gates for S and C outputs

Half Adder simulation

To show this adder circuit works, you’ll discover a simulation under. Easy switches symbolize the A and B inputs. The S and C outputs are represented by LEDs, the place a lit LED means “1” and an unlit LED means “0”.

Half Adder simulation


Do you have got any questions on how this adder circuit works? Let me know within the feedback under.


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