Adder or summer in electronics
Adders in digital electronics are mainly used to add binary numbers or BCD numbers. In general, a distinction can be made between half adders and full adders.
Half Adder (HA)
The half adder is is a digital logic circuit with which you can add two single-digit binary numbers. In addition to two inputs, the half adder also has two outputs. The output S (sum or count value) is the least significant bit (LSB) with the value 20 and the output carry is the most significant bit (MSB) with the value 21.
Logic gate Half Adder – how it works
Full Adder (FA)
With a full adder, you can add three single-digit binary numbers. Therefore, it has three inputs. One input is usually used to carry over the previous calculation stage. The number (2) of outputs is the same as for the half adder. The output S (sum) provides the least significant digit of the result, the output carry the most significant digit.
Let´s develop the logic circuit from the truth table:
Full Adder - Implementation by using logic gates
Addition of multi-digit binary numbers
A 4-bit adder can be used to add two binary numbers with four digits. It is made up of four full adders. If you are sure that no carry from a previous calculation needs to be taken into account, the first stage can also be a half adder. As you can see, this circuit corresponds to a series connection of four adders.
Full Adder for 4-Bit numbers - how it works Animation