The combinational logic circuits are the circuits that contain different types of logic gates. Simply, a circuit in which different types of logic gates are combined is known as a combinational logic circuit. The output of the combinational circuit is determined from the present combination of inputs, regardless of the previous input. The input variables, logic gates, and output variables are the basic components of the combinational logic circuit. There are different types of combinational logic circuits, such as Adder, Subtractor, Decoder, Encoder, Multiplexer, and De-multiplexer.
There are the following characteristics of the combinational logic circuit:
The 'n' input variable comes from the external source while the 'm' output variable goes to the external destination. In many applications, the source or destinations are storage registers.
The half adder is a fundamental component in computer arithmetic, responsible for adding two individual binary digits. When we have two binary digits, A and B, the half adder combines them using a circuit that produces two outcomes: the sum and the carry. The carry accounts for any excess resulting from the addition of these two numbers. This concept is visually illustrated in the block diagram shown below.
Truth Table of Half Adder:
Half Adder - Logic Circuit
The sum S is represented by the Boolean Expression S = A'B + AB' and C = AB
Half adder + Cin = Full Adder
The next truth table shown here demonstrates all the possible outputs for various input combinations with the carry input digit:
Truth Table - Full Adder:
Boolean expression for the full adder is S = A'B'Cin + A'BCin' + AB'Cin' + ABCin and C = A'BCin + AB'Cin + ABCin' + ABCin. This is where A and B are all the possible binary inputs and C is the carry in. For example, if A is 0 and B is 0 and the Cin is 1, then:
S = (0'0'1)+(0'01')+(00'1')+(001) = (111)+(100)+(010)+(001) = (1)+(0)+(0)+(0) = 1
C = (0'01)+(00'1)+(001')+(001) = (101)+(011)+(000)+(001) = (0)+(0)+(0)+(0) = 0
S = 1 and C = 0
Full Adder - Logic Circuit
A subtractor serves the purpose of deducting one numerical value from another. In the context of binary arithmetic, subtraction is accomplished using the 1's complement and 2's complement representations of the numbers involved. This process requires the manipulation of three key binary bits: the minuend (X), the subtrahend (Y), and the borrow (Bi), which is derived from the preceding bit's result. The outcome of this operation is twofold: it yields the difference (D) and also provides the next borrow bit (Bout).
Half Subtractor - Logic Circuit
Truth Table - Half Subtractor
The Boolean expressions are as follows:
D = X'Y + XY'
Bout = X'Y
Example: If our inputs X and Y are 0 and 1, then compliment of 0 is 1 and vice versa.
D = (0'1)+(01') = (11)+(00) = 1 and Bout = (0'1) = (11) = 1
Full Subtractor - Logic Circuit
Truth Table - Full Subtractor:
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