Boolean Theorems

Duality Principle: Dual of an expression can be obtained by : Changing all + with . Complement 0’s and 1’s i.e. 1’=0 and 0’=1 Keep the variable sam (i.e. do not complement the variable) Example: Find the dual of : A(B+C) = AB + AC Solution: Find the Dual of F(xyz)=(x+y) (x+z)(y+z) Solution:             (x+y) […]

Axioms and Laws of Boolean Algebra

Boolean Algebra Axioms and Laws of Boolean Algebra Boolean algebra devised in 1864 by George Boole, is a system of mathematical logic. It is an algebraic system consisting of a set of element (0,1) associated with a Boolean variable and two binary operators AND and OR and a uniry operator NOT. In mathematics, an identity is a […]

Hamming Code

Hamming Code Hamming code is an improvement over the other parity systems, this approach enable us to detect one bit error that might get introduced during transmission in every byte of information, However, this is done at the cost of increased data size due to introduction of multiple parity bits. Calculating the Hamming Code   […]

Parity Code

Error Detecting Codes: When we transmit a computer code over a medium, the possibility of a bit being lost due to transient or any other reason become the point of interest. During data sharing, the flow of information on the channel require high data integrity for the  system to properly work on that data. So, […]

Computer Codes

Computer Codes: The second category of codes are those codes which cannot be represented by any analytical relation, hence these codes are also called as non-analytical code.Non-Analytical code. These are the following codes: Non-Weighted Codes: Excess-3 Codes, Gray Codes, BCD greater than 4-bits Self Complementing codes: 2421, 5211, Excess-3 (XS-3) Sequential Codes: 8421 and XS-3 […]

Signed Number Systems

Signed Number System In signed number systems, a number is represented with two parts; one the sign bit, and the rest bits denote the magnitude of the number. Signed number are represented using the following representation: Sign and Magnitude number system: 1’s complement Number System 2’s Complement Number System Sign and Magnitude number system In […]

Introduction to Analog and Digital System

Analog signal and Digital signals Everything in real world is analog, the audio we hear, the scene we see in front of our eyes, the environment parameters like, humidity, temperature, atmospheric pressure and so on are all example of analog signals. In earlier time may be way back in 80’s and before, these analog quantity […]

Number System

Number System: In every day life we encounter with objects that are to be counted and written to be understood by all. The represented number also may require addition, subtraction etc. So, number system is a way of representing the count of some objects or countable things using some well define symbols and on which […]

8051 LOGICAL INSTRUCTIONS

Logical Type Instruction   ANL Instruction ANL Performs bit wise AND operation between the specified byte. When used to modify an output port, the value used as the port data will be read from the output data latch, not the input pins of the port. format example Opcode/Encoding Flags affected ANL A, #data ANL A, […]

8051 Rotate Instructions

ROTATE INSTRUCTIONS These instruction rotate the accumulator left, or right with or without carry. The instructions are RR, RRC, RL, RLC. RL Instruction The RL instruction rotates accumulator left one bit left Figure shows how the bits rotate left internally and then bit-7 to bit-0 No flags are affected by this instruction Figure 7.1 : Rotate left […]

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