Electrical Engineering ⇒ Topic : Full Adder Circuits
FULL ADDER CIRCUITS
Contrary to the half adder circuit, full adder is meant to add two bits along with the carry from the former bit addition. When more than two binary digits are to be added, several half adders are inadequate because the half adder has no input to handle carries from the preceding addition.
Consider the following binary summation
As shown earlier, the carries generated in each column must be considered during the addition process. Therefore, adder circuitry capable of adding the contents of two registers must include provision for handling carries as well as binary bits. So, there must be three inputs to each stage of multi-digit adder except for the stage of the least significant bit. Table (1) shows the truth table for sum and carry
Figure (2) shows the K-map for sum and carry of Table (1).
From Figure 2 (a),
From Figure 2 (b),
From the above K-map for the carry, it can be simplified to the following:
Now using these two boolean expressions for the sum and carry, we can design logic circuit for adding two bits as shown in Figure (3).
Figure (3) Full adder.
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