Fundamentals of Digital Logic and Microcontrollers, 6th Edition

Chapter 4Combinational Logic

4.1 Basic Concepts

Digital logic circuits can be classified into two types: combinational and sequential. A combinational circuit is designed using logic gates in which application of inputs generates the outputs at any time. An example of a combinational circuit is an adder, which produces the result of addition as output upon application of the two numbers to be added as inputs.

A sequential circuit, on the other hand, is designed using logic gates and memory elements known as flip-flops. Note that the flip-flop is a one-bit memory. A sequential circuit generates the circuit outputs based on the present inputs and the outputs (states) of the memory elements. The sequential circuit is basically a combinational circuit with memory. Note that a combinational circuit does not require any memory (flip-flops),whereas sequential circuits require flip-flops to remember the present states. A counter is a typical example of a sequential circuit. To illustrate the sequential circuit, suppose that it is desired to count in the sequence 0, 1, 2,3, 0, 1,… and repeat. In binary, the sequence is 00, 01, 10, 11, 00, 01, …, and so on. This means that a two-bit memory using two flip-flops is required for storing the two bits of the counter because each flip-flop stores one bit. Let us call these flip-flops with outputs A and B. Note that initially A = 0 and B = 0. The flip-flop changes outputs upon application of a clock pulse. With appropriate inputs to the flip-flops ...