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How does Half Adder work with the truth table?

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How Half Adder Works?

How does Half Adder work with the truth table? Half Adder is a combinational logic circuit that adds two binary digits i.e 0 and 1.Combinational circuits are half adder and full adder, subtractor, encoder, decoder, multiplexer, and demultiplexer. 

What is Combinational Logic Circuits

  • The output of a combinational circuit at any instant of time depends only on the levels present at input terminals.
  • The combinational circuit does not use any memory. The previous state of input does not have any effect on the present state of the circuit.
  • A combinational circuit can have an n number of inputs and an n number of outputs.

The block diagram is shown below in which A and B two inputs and S(Sum) and C(Carry) are outputs.

  • Half Adder is a combinational logic circuit.
  • It is used for the purpose of adding two single-bit numbers.
  • It contains 2 inputs and 2 outputs (sum and carry).

Keep in mind Half Adder is Combinational logic circuit whose output at any instant in time depends only on the combination of its inputs. Unlike Sequential Logic Circuits whose outputs are dependent on both their present inputs and their previous output state giving them some form of Memory.

Block diagram of Half Adder

The addition of 2 bits is done using a combination circuit called a Half adder. The input variables are augend and addend bits and the output variables are sum & carry bits. A and B are the two input bits.

How Full Adder Works?

There are two inputs and two outputs in a Half Adder. Inputs are named as A and B, and the outputs are named as Sum (S) and Carry (C). The Sum is X-OR of the input A and B. Carry is AND of the input A and B. With the help of a half adder, one can design a circuit that is capable of performing simple addition with the help of logic gates.

Circuit diagram of Half Adder

As shown in the above circuit diagram there are two gates that are used X-OR and AND Gate. X-OR gate generates Sum output and AND Gate gives Carry output. In the above diagram, A input connected both X-OR gate and AND Gate. While B input connected both X-OR Gate and AND Gate.

Now a days every electronics circuits use Adders. because most circuits like laptop, LCD TV, mobiles and other electronics equipment’s use adders.

Truth table of Half Adder
  • Above is the truth table of half adder in which we can see that if A and B inputs are zeros SUM and CARRY both are zeros.
  • When A is 0 and B is 1 then Sum is 1 and Carry is 0.
  • When A is 1 and B is 0 then Sum gives 1 output and Carry gives 0 output.
  • When both A and B both inputs are 0s then Sum gives 0 and Carry gives 1 output.

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