Designing Combinatorial Circuits

The design of a combinational circuit starts from the verbal outline of the problem and ends with a logic circuit diagram or a set of Boolean functions from which the Boolean function can be easily obtained. The procedure involves the following steps:
- The problem is stated
- The number of available input variables and required output variables is determined.
- The input and output variable are assigned their letter symbol
- The truth table that defines the required relationship between the inputs and the outputs is derived.
- The simplified Boolean function for each output is obtained
- The logic diagram is drawn.

Example of combinational circuit
Adders
In electronics, an adder or summer is a digital circuit that performs addition of numbers. In modern computers adders reside in the arithmetic logic unit (ALU) where other operations are performed. Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where twos complement or ones complement is being used to represent negative numbers, it is trivial to modify an adder into an adder-subtracter. Other signed number representations require a more complex adder. -Half Adder A half adder is a logical circuit that performs an addition operation on two binary digits. The half adder produces a sum and a carry value which are both binary digits. A half adder has two inputs, generally labelled A and B, and two outputs, the sum S and carry C. S is the two-bit XOR of A and B, and C is the AND of A and B. Essentially the output of a half adder is the sum of two one-bit numbers, with C being the most significant of these two outputs. The drawback of this circuit is that in case of a multibit addition, it cannot include a carry. Following is the truth table for a half adder:The design of a combinational circuit starts from the verbal outline of the problem and ends with a logic circuit diagram or a set of Boolean functions from which the Boolean function can be easily obtained. The procedure involves the following steps:
- The problem is stated
- The number of available input variables and required output variables is determined.
- The input and output variable are assigned their letter symbol
- The truth table that defines the required relationship between the inputs and the outputs is derived.
- The simplified Boolean function for each output is obtained
- The logic diagram is drawn.

Example of combinational circuit
Adders
In electronics, an adder or summer is a digital circuit that performs addition of numbers. In modern computers adders reside in the arithmetic logic unit (ALU) where other operations are performed. Although adders can be constructed for many numerical representations, such as Binary-coded decimal or excess-3, the most common adders operate on binary numbers. In cases where twos complement or ones complement is being used to represent negative numbers, it is trivial to modify an adder into an adder-subtracter. Other signed number representations require a more complex adder. -Half Adder A half adder is a logical circuit that performs an addition operation on two binary digits. The half adder produces a sum and a carry value which are both binary digits. A half adder has two inputs, generally labelled A and B, and two outputs, the sum S and carry C. S is the two-bit XOR of A and B, and C is the AND of A and B. Essentially the output of a half adder is the sum of two one-bit numbers, with C being the most significant of these two outputs. The drawback of this circuit is that in case of a multibit addition, it cannot include a carry. Following is the truth table for a half adder: