7. LECTURE NOTES: (40 Minutes)
Logic circuits are the basis for modern digital computer systems. The term
digital refers to the fact that the signal is limited to only a few possible values. In general,
digits signals are represented by only two possible voltages on a wire - 0 volts (which are
called "binary 0", or just "0") and 5 volts (which are call by "binary 1", or just "1"). We
sometimes call these values "low" and "high", or "false" and "true".
Need of digital systems
More complicated signals can be constructed from 1s and 0s by stringing them
end-to-end, like a necklace.
If we put three binary digits end-to-end, we have eight possible combinations:
000, 001, 010, 011, 100, 101, 110 and 111. In principle, there is no limit to use
binary digits, so signals can be as complicated as one like
Major topics in Boolean algebra and logic gates
1. Review of number systems-is a natural choice for representing the behavior of
circuits that operate in one of two states (on or off, 1 or 0)
2. Arithmetic Operations-It is imperative to understand that the type of numeration
system used to represent numbers has no impact upon the outcome of any
arithmetical function (addition, subtraction, multiplication, division, roots,
powers, or logarithms).
3. Binary codes- The alphabetic data, numeric data, alphanumeric data, symbols,
sound data and video data, all are represented as combination of bits in the
4. Boolean algebra and theorems-The English mathematician George Boole (18151864) sought to give symbolic form to Aristotle's system of logic.
5. Boolean functions- Boole wrote a treatise on the subject in 1854, titled An
Investigation of the Laws of Thought, on Which Are Founded the Mathematical
Theories of Logic and Probabilities, which codified several rules of relationship
between mathematical quantities limited to one of two possible values: true or
false, 1 or 0
6. Simplifications of Boolean functions using Karnaugh map and tabulation
methods- A K-map consists of a grid of squares, each square representing one
canonical minterm combination of the variables or their inverse
7. Logic gates-A logic gate, or simply gate, is a special circuit designed to input
and output logic level voltages (voltages intended to represent binary bits).
8. NAND and NOR Implementations- Universal gates are the ones which can be
used for implementing any gate like AND, OR and NOT, or any combination of
these basic gates; NAND and NOR gates are universal gates
Sanjay Kumar Suman, L.Bhagyalakshmi, S.Porselvi, “Digital Principles And System
Design”,Vijay Nicole Pubilcations
The digital system is used to represent various types of computer data. It is used
to design various circuits in real time as controller, indicator etc.
CS6201-DIGITAL PRINCIPLES AND SYSTEM DESIGN