Multiplexers and De-Multiplexers STLD/Digital Electronics by Ravinder Nath Rajotiya - August 18, 2019August 23, 20190 Introduction to Multiplexer: A multiplexer, also called as a data selector, is a combinational circuit used to select information from one of the many input sources and directs it to a single output line. A multiplexer has several data input lines but only one output. Control or selection lines are used for selecting one of the input lines. Multiplexers come in sizes 2N x1 (like 2x1, 4x1, 8x1,16x1 etc). In general, a multiplexer has 2N input lines, N control lines and 1 output line. Figure-1 shows the General block diagram of a multiplexer. 2x1 Multiplexer A 2x1 multiplexer will have two inputs, one selection or control line and one output. The output equation of a 2x1 multiplexer is : Y= I1.S + I0.S’ Multiplexer may also have an active high or
Adder Circuits STLD/Digital Electronics by Ravinder Nath Rajotiya - August 14, 2019August 17, 20190 Adder Circuits An adder is a combinational circuit that adds multi-bit (two or more). Different types of adders are: Half Adder : A combinational circuit that adds 2-bits Full Adder : A combinational circuit that adds 2-bits and a carry from the previous stage of addition. Ripple Carry Adder/ or Carry Propagate Adder: An adder that add multi-bit numbers. Carry-Look-Ahead Adders: A type of fast adders that pre-computes the carry bit. Serial Adder: An adder that takes the serial data inputs, computes the sum and carry for bit Ai, Bi, Ci produces Si; each time an addition is performed the sum bit shifted in a shifter. The content of shift register gives the Sum output. Half Adder: A half adder circuit is a logic circuit that
Introduction to Karnaugh-Map STLD/Digital Electronics by Ravinder Nath Rajotiya - August 7, 2019May 10, 20210 Karnaugh Map (K-map) K-Map is a pictorial representation of the Boolean function. It is a systematic method of simplifying the Boolean expression. A K-Map is an arrangement of the adjacent cell , each cell representing the minterm or the maxterm of the SOP or the POS equations. The number of adjacent cells in a K-Map depends on the number of input variables in an equation. The number of cell equals 2N where N is the number of input variables. Let us see how the minterm or the maxterms of the SOP or POS equations are represented. Two variable K-Map Table in figure-1 on the left is a truth table for two input variables. The output is shown in column marked ‘F’. m0, m1, m2,
Boolean Function STLD/Digital Electronics by Ravinder Nath Rajotiya - August 6, 2019May 10, 20210 Boolean Functions The following steps are generally followed while designing the logic circuits using Boolean functions. Analysis of the given statement of the problem to find the number of variables Writing the truth table from the given statement Conversion of the truth table into a logic function/ Boolean expression using standard product of sums(SOP) or product of sums (POS) Simplify the Boolean expression Create the logic circuit using logic gates SOP and POS equations Sum of Product (SOP) equation The SOP equations are formed by ORing the product or the min-terms. Formation of Minterm and Maxterm A B C Minterm(mi) Maxterms(Mi) 0 0 0 A’B’C’ =m0 A+B+C =M0 0 0 1 A’B’C =m1 A+B+C’ =M1 0 1 0 A’BC’ =m2 A+B’+C =M2 0 1 1 A’BC =m3 A+B’+C’ =M3 1 0 0 AB’C’ =m4 A’+B+C =M4 1 0 1 AB’C =m5 A’+B+C’ =M5 1 1 0 ABC’ = m6 A’+B’+C =M6 1 1 1 ABC = m7 A’+B’+C’ =M7 Min terms The input combinations for which the output equals ‘1’ is called
Boolean Theorems STLD/Digital Electronics by Ravinder Nath Rajotiya - August 6, 2019May 10, 20210 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) (x+z)(y+z) = (xx+xz+xy +yz)(y+z) = (x+xz+xy+yz)(y+z) = (x +xy +yz )(y+z) = (x+yz)(y+z) = xy +xz + yyz + yz = xy + xz + yz Also dual of (x+y) (x+z)(y+z) = xy + xz + yz Therefore, we find that in this case dual of a function is the function itself 3. For n variables expression haw many total dual functions are possible Solution: Which of the following is TRUE S1: The dual of NAND function is NOR S2:The dual of