Monday, 11 December 2017

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DIGITAL LOGIC CIRCUITS (PART 2)

The Full Adder
   In the previous article, the half adder was introduced, in this article, I am mainly going to be focussing on the full adder. Before moving forward I would for you to go back and do a little revision of the half adder.


THE FULL ADDER

   The full adder unlike the half adder can add larger binary numbers, it takes in three inputs and gives out a sum and a carry output. The  major difference between the full and half adder is the fact that the half adder is only used to add least significant bits (LSB)  without accounting for the carryout of the previous addition. While the full adder is used to add up most significant bits (MSB) and  LSBs and also taking into account the carry out from the previous additions.

   At this point it will be wise for us to recall the procedures for adding larger binary numbers; firstly, we begin with the addition of the LSBs of the two numbers, we record the sum under the LSB column and take the carry, if any to the next higher column bits. As a result, when we add the next adjacent higher column bits, we would be required to add three bits if there were a carry from the previous addition. We continue with the same procedure of adding the next two LSBs and the carry if there is, until we get to the MSB. Therefore, if want a hardware that can add larger binary numbers, it is therefore of utmost importance that the full adder circuit must be implemented. The truth table and equations coupled with the circuit is shown below;

A
B
Cin
Sum
Cout
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
Fig.1.  Truth Table


Fig.2.  Equations of Full adder


Fig.2. CIRCUIT DIAGRAM


    
   The full adder described above forms the basic building block of binary adders. However, a single full adder circuit can be used to add one bit binary numbers only. A  cascade arrangement of these adders can be used to construct adders capable of adding binary numbers with a large number of bits. A five bit binary adder would require four full adders.
    This brings us to the end of this part, if you want the video on how to simulate the full adder to add larger number of bits, please comment below for the link.

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