Discussion

    At the heart of digital computers and calculators is the arithmetic unit. Depending on the system, this unit can range in complexity from very simple such an adder, to a unit that possesses the capabilities of computing values for special functions such as trigonometric and logarithmic functions. No matter how complex the unit is, its most important functions is still addition.

    The primary building blocks in adder circuits are half adders and full adders.

    Full Adder

    The Truth table for a full adder that shows all the input and output values for all possible case is in FIGURE 1.
 

 
Augend bit input
A
Addend bit input
B
Carry bit input
CIN
Sum bit output
S
Carry bit output
COUT
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
 
 
FIGURE 1    Truth table and block diagram for a Full Adder circuit.
 
 
FIGURE 2    Complete circuitry for a full adder.