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BINARY ARTHMETIC

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Binary Arithmetic Binary arithmetic is used in digital systems mainly because the numbers (decimal and floating-point numbers) are stored in binary format in most computer systems. All arithmetic operations such as addition, subtraction, multiplication, and division are done in binary representation of numbers. It is necessary to understand the binary number representation to figure out binary arithmetic in digital computers.      * Binary Addition      * Binary Subtraction      * Binary Multiplication      * Binary Division Binary Addition:           It is a key for binary subtraction, multiplication, division. There are four rules of binary addition. fourth case, a binary addition is creating a sum of (1 + 1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next column. Example − Addition Binary Subtraction: Subtraction and Borrow, these two words will be u...
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LOGIC GATES

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Logic Gates.   Logic gates Digital systems are said to be constructed by using logic gates. These gates are the AND, OR, NOT, NAND, NOR, EXOR and EXNOR gate Basic Gates:           *AND GATE           *OR GATE           *NOT GATE     Universal Gates:           *NOR GATE           *NAND GATE Exclusive Gates:           *EXOR GATE           *EXNOR GATE AND GATE: Logic diagram Truth Table The  AND gate  is a basic digital  logic gate  that implements  logical conjunction  - it behaves according to the  truth table  to the right. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If none or not all inputs to the AND gate are HIGH, LOW output results. The function can be extended to any number of inputs.       OR Ga...
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Boolean algebra

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BOOLEAN ALGEBRA  Boolean algebra was introduced by  George Boole  in his first book  The Mathematical Analysis of Logic  (1847), and set forth more fully in his  An Investigation of the Laws of Thought  (1854). [2]  According to  Huntington , the term "Boolean algebra" was first suggested by  Sheffer  in 1913, [3]  although  Charles Sanders Peirce  gave the title "A Boolean Algebra with One Constant" to the first chapter of his "The Simplest Mathematics" in 1880. [4]  Boolean algebra has been fundamental in the development of  digital electronics , and is provided for in all modern programming languages. It is also used in  set theory  and  statistics . [5 Truth Tables for the Laws of Boolean Definition of Boolean algebra:   Boolean algebra is a six-tuple consisting of a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary o...
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