# Combinational Circuits Implementations with Fixed Logic

#### Abstract

Combinational (combinatorial) circuits realize Boolean functions and deal with digitized signals, usually denoted by 0s and 1s. The behavior of a combinational circuit is memoryless; that is, given a stimulus to the input of a combinational circuit, a response appears at the output after some propagation delay, but the response is not stored or fed back. Simply put, the output depends solely on its most recent input and is independent of the circuit’s past history. Design of a combinational circuit begins with a behavioral specification and selection of the implementation technique. These are then followed by simplification, hardware synthesis, and verification. Combinational circuits can be specified via Boolean logic expressions, structural descriptions, or truth tables. Various implementation techniques, using fixed and programmable components, are outlined in the rest of this article. Combinational circuits implemented with fixed logic tend to be more expensive in terms of design effort and hardware cost, but they are often both faster and denser and consume less power. They are thus suitable for high-speed circuits and/or high-volume production. Implementations that use memory devices or programmable logic circuits, on the other hand, are quite economical for low-volume production and rapid prototyping, but may not yield the best performance, density, or power consumption. Simplification is the process of choosing the least costly implementation from among feasible and equivalent implementations with the targeted technology. For small combinational circuits, it might be feasible to do manual simplification based on manipulating or rewriting logic expressions in one of several equivalent forms. In most practical cases, however, automatic hardware synthesis tools are employed that have simplification capabilities built in. Such programmed simplifications are performed using a mix of algorithmic and heuristic transformations. Verification refers to the process of ascertaining, to the extent possible, that the implemented circuit does in fact behave as originally envisaged or specified. A half adder is a simple example of a combinational circuit. The addend, augend, carry, and sum are all single binary digits or bits. If we denote the addend as A and the augend as B, the Boolean function of carry-out Co and sum S can be written as

### Cite this paper

@inproceedings{Webster2010CombinationalCI, title={Combinational Circuits Implementations with Fixed Logic}, author={J. Webster}, year={2010} }