Combinational Logic Circuit PDF

Digital Logic and Digital Systems COMBINATIONAL VS SEQUENTIAL LOGIC/FIELD PROGRAMMABLE GATE ARRAYS (FPGAS) Combinational vs. Sequential Logic/Field ProgrammableGate Arrays (FPGAS) FUNDAMENTAL COMBINATIONAL  What is a Gate? ❑The building blocks used to create digital circuits. ❑Combina...

Digital Logic and Digital Systems COMBINATIONAL VS SEQUENTIAL LOGIC/FIELD PROGRAMMABLE GATE ARRAYS (FPGAS) Combinational vs. Sequential Logic/Field ProgrammableGate Arrays (FPGAS) FUNDAMENTAL COMBINATIONAL  What is a Gate? ❑The building blocks used to create digital circuits. ❑Combination of transistors that performs binary logic. ❑There three (3) elementary logic gates and a range of other simple gates. ❑Each gate has its own logic symbol which allows complex functions to be represented by a logic diagram. ❑The function of each gate can be represented by a truth table or using Boolean notation. Types of Logic Gates  NOT Gate ❑Accepts one input value and produces one output value. ❑If the input value for a NOT gate is 0, the output value is 1, and if the input value is 1, the output value is 0. ❑A NOT gate is sometimes referred to as an inverter because it inverts the input value. NOT Gate AND Gate OR Gate NAND and NOR Gates XOR Gate XNOR Gate BUFFER Gate  Combinational Logic Circuit (CLC) ❑The digital logic circuits whose outputs can be determined using the logic function of current state input.  Combinational Logic Circuit (CLC) ❑Basically made up of digital logic gates like AND gate, OR gate, NOT gate and the universal (NAND and NOR gates). ❑All these gates are combined together to form a complicated switching circuit. ❑Examples: Adder Subtractor Converter Encoder/Decoder Multiplexer/Demultiplexer Classification of CLC  Classification of CLC ❑Combinational circuits are used in a wide range of applications such as calculators, digital measuring techniques, computers, digital processing, automatic machine control, industrial processing, digital communications, and so on. ❑For various applications, various types of combinational logic circuits are used. ❑Combinational logic circuits are classified into three types based on their function, namely Arithmetic and logic circuits, data transmission circuits, and code converter circuits.  Characteristics of CLC ❑At any instant of time, the output of combinational logic circuit depends only on the present input terminals. ❑Memory elements is absent in the combinational circuit. The combinational circuit doesn’t have any backup or previous memory. ❑No clock signal is required in combinational circuit.  Characteristics of CLC ❑The n number of inputs and m number of outputs are possible in combinational logic circuits. The n input variable comes from the external source while the m output variable goes to the external destination. In many applications, the source or destinations are storage registers. Combinational Logic Circuit Classification Arithmetic and Logical Functions  Half Adder ❑ A combinational logic circuit with two inputs and two outputs. ❑ It is designed to add two single bit binary number A and B. ❑ It is the basic building block for addition of two single bit numbers. ❑ The circuit has two outputs carry and sum.  Half Adder In the above table, 1. 'A' and' B' are the input states, and Logic Circuit Diagram 'sum' and 'carry' are the output states. 2. The carry output is 0 in case where both the inputs are not 1. 3. The least significant bit of the sum is defined by the 'sum' bit. The SOP form of the sum and carry are as follows: Sum = A’B+AB' Carry = AB  Half Adder Application of Half Adder in Digital Logic ❑ Arithmetic circuits: Half adders are utilized in number- crunching circuits to add double numbers. At the point when different half adders are associated in a chain, they can add multi-bit double numbers. ❑ Data handling: Half adders are utilized in information handling applications like computerized signal handling, information encryption, and blunder adjustment. ❑ Address unraveling: In memory tending to, half adders are utilized in address deciphering circuits to produce the location of a particular memory area.  Half Adder Application of Half Adder in Digital Logic ❑ Encoder and decoder circuits: Half adders are utilized in encoder and decoder circuits for computerized correspondence frameworks. ❑ Multiplexers and demultiplexers: Half adders are utilized in multiplexers and demultiplexers to choose and course information. ❑ Counters: Half adders are utilized in counters to augment the count by one.  Full Adder ❑ Performs the addition of three bits at a time. Block Diagram  Full Adder Sum: ❑ Perform the XOR operation of input A and B. ❑ Perform the XOR operation of the outcome Carry: with carry. So, the sum is (A 1. Perform the 'AND' operation of input A and B. XOR B) XOR 2. Perform the 'XOR' operation of input A and B. Cin which is also 3. Perform the 'OR' operations of both the represented as: outputs that come from the previous two (A ⊕ B) ⊕ Cin steps. So the 'Carry' can be represented as: A.B + (A ⊕ B)  Half Subtractor ❑ A combination circuit with two inputs and two outputs difference (diff) and borrow. ❑ Produces the difference between the two binary bits at the input and also produces a output (borrow) to indicate if a 1 has been borrowed. ❑ In the subtraction (A-B), A is called the Minuend bit and B is called as Subtrahend bit. Half Subtractor The SOP form of the Diff and Borrow is as follows: Diff= A'B+AB' Borrow = A'B In the above table, 'A' and 'B' are the input variables whose values are going to be subtracted. The 'Diff' and 'Borrow' are the variables whose values define the subtraction result, i.e., difference and borrow. The first two rows and the last row, the difference is 1, but the 'Borrow' variable is 0. The third row is different from the remaining one. When we subtract the bit 1 from the bit 0, the borrow bit is produced.  Half Subtractor Application of Half Subtractor in Digital Logic: ❑ Calculators: Most mini-computers utilize advanced rationale circuits to perform numerical tasks. A Half Subtractor can be utilized in a number cruncher to deduct two parallel digits from one another.  Half Subtractor Application of Half Subtractor in Digital Logic: ❑ Alarm Frameworks: Many caution frameworks utilize computerized rationale circuits to identify and answer interlopers. A Half Subtractor can be utilized in these frameworks to look at the upsides of two parallel pieces and trigger a caution in the event that they are unique.  Half Subtractor Application of Half Subtractor in Digital Logic: ❑ Automotive Frameworks: Numerous advanced vehicles utilize computerized rationale circuits to control different capabilities, like the motor administration framework, stopping mechanism, and theater setup. A Half Subtractor can be utilized in these frameworks to perform computations and examinations.  Half Subtractor Application of Half Subtractor in Digital Logic: ❑ Security Frameworks: Advanced rationale circuits are usually utilized in security frameworks to identify and answer dangers. A Half Subtractor can be utilized in these frameworks to look at two double qualities and trigger a caution in the event that they are unique.  Half Subtractor Application of Half Subtractor in Digital Logic: ❑ Computer Frameworks: Advanced rationale circuits are utilized broadly in PC frameworks to perform estimations and examinations. A Half Subtractor can be utilized in a PC framework to deduct two paired values from one another.  Full Subtractor ❑ The full subtractor is used to subtract three 1- bit numbers A, B, and C, which are minuend, subtrahend, and borrow, respectively. ❑ The full subtractor has three input states and two output states i.e., difference (diff) and borrow.  Full Subtractor Truth Table In the truth table, A and B are the input variables. These variables represent the two significant bits that are going to be subtracted. Borrowin is the third input which represents borrow. The Diff and Borrow are the output variables that define the output values. The eight rows under the input variable designate all possible combinations of 0 and 1 that can occur in these variables.  Full Subtractor Borrow: Perform the AND operation of the inverted input A and B. Perform the XOR operation of input A and B. Perform the OR operations of Diff: both the Perform the XOR operation of input A and B. outputs that Perform the XOR operation of the outcome with come from the Borrow. So, the difference is (A XOR B) XOR Borrowin previous two which is also represented as: steps. So the (A ⊕ B) ⊕ Borrowin 'Borrow' can be represented as: A'.B + (A ⊕ B)'  Comparator ❑ A combinational circuit that compares two digital or binary numbers in order to find out whether one binary number is equal, less than, or greater than the other binary number. ❑ Logically design a circuit for which there will be two inputs one for A and the other for B and have three output terminals, A > B condition, A = B condition, A < B condition.  Comparator ❑ 1-Bit Magnitude Comparator From the above truth table logical expressions for each output can be expressed as follows. A>B: AB’ A