A combinational circuit is a connected arrangement of logic gates with a set of inputs and outputs. At any given time the binary values of outputs are a function of the binary combination of the inputs.
Now below i will discuss two basic arthamatic circuits. I take these as my example of basic circuits. Before going to in this you need to have some basic idea about logical gates go to basic logical gates my previous post.
Half Adder:
The most basic digital arithmetic circuits is the addition of two binary digits. A combinational circuit that performs the arithmetic addition of tow bits is called a half adder. the input variables of a half adder anre called the augend and addend bits. The output variables the sum and carry.It is necessary to specify two out put variables because the of 1+1 is binary 10, which has tow digits. We assign symbols x and y to the tow input variables. The C output is 0 unless both imputs are 1. The S output represents the least significant bitof the sum.
S=x`y+xy`
C=xy
Truth table
x y C S
0 0 0 0
0 1 0 1
1 0 0 1
1 1 1 0
Full Adder:
A Full-adder is a combinational circuit that forms the arithmetic sum of three input bits. It consists of three inputs and two outputs. Two of the input variables, denoted by A and B, represent the two significant bits to be added. The thired input Cin represents the carry from the previous lower significatn position. Two outputs are necessary because the arithmetic sum o three dinary digits ranges in value from 0 to3, and binary 2 or 3 needs two digits. The two outputs are designated by the symbols S(for sum) and Cout (for carrry). The boolean expression of Full adder is as follows.
truth tableInputs | Outputs | |||
|---|---|---|---|---|
| A | B | Cin | Cout | S |
| 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 1 | 1 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
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