
Learn how to convert numbers between bases by first translating any base to decimal, then converting decimal to the target base, with examples of binary, hex, and other bases.
Explore the weighted, positional concept of number systems, from decimal base ten to binary and octal, including base values, decimal point positions, and basics of conversion.
Learn how to perform addition across numeral systems, including decimal, base eight, and binary, using carry rules and standard procedures, and apply the same method to subtraction operations.
Explain binary to gray conversion using the reflective gray code, highlighting single-bit transitions, cyclic sequencing, and the reflection principle for generating gray codes from binary numbers.
Explore how to compute complements in various bases by subtracting from the maximum possible number or using one's and sixteen's complements, with base-2, base-8, base-16, and decimal examples.
Explore unsigned binary representation and signed two's complement encoding for positive and negative numbers, with conversions between binary and decimal and the typical 8-bit range of minus 128 to 127.
Explore basic boolean operations and reading and simplifying boolean expressions with boolean algebra. Use associativity and absorption to reduce circuit size and literals, boosting digital logic speed.
design any logical expression using nand gates by converting to sop form and exploiting universal nand logic, with two-input and multi-input design and proper gate arrangement.
Explore variable k-map concepts for sop expressions, grouping cells into quads and octets, and deriving simplified expressions like a + b in three-variable maps.
Explains solving three-variable k-map problems by forming optimal groups (quads and pairs), deriving simplified expressions such as b+c, and identifying prime implicants and essential prime implicants.
Explore three-variable k-map problems, identify don’t-care conditions, form groups of eight or four cells, and derive simplified expressions using prime implicants in digital system design.
Apply variable k-map techniques to simplify boolean expressions by forming groups of cells, identifying prime implicants and essential prime implicants, and deriving the minimal expression.
This Course deals with the basic number system ( types of number system, conversions, BCD code, Gray code, Excess-3 code and binary data representation) .
This Course Explains Boolean operations, Sum Of Product and Product Of Sum, Boolean theorems and Logic Gates(NAND,NOR).
This course deals with Boolean expression simplification methods ( K-MAP and tabulation method )
you will learn:
1. Number Systems, Conversions, Gray code, BCD code,Excess-3 code, Binary Data Representation, different Binary codes.
2. Boolean Algebra : Boolean Theorems, SOP & POS, Venn diagrams, Duality Theorem, De-Morgan's Theorem, residue theorem, absorption theorem. ( The concept of Boolean algebra was first introduced by George Boole in his book, The Mathematical Analysis of Logic, and further expanded upon in his book, An Investigation of the Laws of Thought. Since its concept has been detailed, Boolean algebra's primary use has been in computer programming languages. Its mathematical purposes are used in set theory and statistics.)
3. Logic Gates : AND,OR, NOT, NAND, NOR, EX-OR, EX-NOR Gates, Design of digital circuits using NAND gates and NOR Gates, Implementation of all the gates using NAND & NOR gates. ( Logic gates are the basic building blocks of any digital system. It is an electronic circuit having one or more than one input and only one output. The relationship between the input and the output is based on a certain logic ).
4. K-Map( 2 - variable, 3 - variable, 4 - variable ). A Karnaugh map (K-map) is a pictorial method used to minimize Boolean expressions without having to use Boolean algebra theorems and equation manipulations. A K-map can be thought of as a special version of a truth table .