Numbering System

Many number systems are in use in digital technology. The most common are the decimal, binary, octal, and hexadecimal systems.

Logic Circuits
Boolean algebra is ideal for expressing the behavior of logic circuits.
A circuit can be expressed as a logic design and implemented as a collection of individual connected logic gates.

Algebraic Manipulation

Minterms and Maxterms

Any boolean expression may be expressed in terms of either minterms or maxterms.

Boundedness Law
X + 1 = 1
X . 0 = 0

Symbolic Logic

Boolean algebra derives its name from the mathematician George Boole. Symbolic Logic uses values, variables and operations 

Boolean Function Implementation
Earlier we had seen that it is possible to implement Boolean functions using decoders. In the same way it is also possible to implement Boolean functions using muxers and de-muxers.

De-multiplexers

They are digital switches which connect data from one input source to one of n outputs.

Multiplexer

A multiplexer (MUX) is a digital switch which connects data from one of n sources to the output. A number of select inputs determine which data source is connected to the output. 

Encoders
An encoder is a combinational circuit that performs the inverse operation of a decoder. If a device output code has fewer bits than the input code has, the device is usually called an encoder. e.g. 2ⁿ-to-n, priority encoders.

Decoders
A decoder is a multiple-input, multiple-output logic circuit that converts coded inputs into coded outputs, where the input and output codes are different; e.g. n-to-2n, BCD decoders.

Introduction
Combinatorial Circuits are circuits which can be considered to have the following generic structure.

K Master Slave Flip-Flop

All sequential circuits that we have seen in the last few pages have a problem (All level sensitive sequential circuits have this problem). 

RS Latch with Clock
We have seen this circuit earlier with two possible input configurations: one with level sensitive input and one with edge sensitive input. The circuit below shows the level sensitive RS latch. 

Latches and Flip-Flops

There are two types types of sequential circuits.

Concept of Sequential Logic

A sequential circuit as seen in the last page, is combinational logic with some feedback to maintain its current value, like a memory cell.

To understand the basics let's consider the basic feedback logic circuit below, which is a simple NOT gate whose output is connected to its input.