Magnitude Comparator: A magnitude comparator is a combinational circuit that compares two binary numbers and determines their relative magnitude. The schematic block diagram in figure-1 has two inputs and three outputs. It compares two numbers for equality, less than and greater than conditions. Depending on the comparison, one of the output will be true and the others will be false.   The table-1 gives the function of the two 1-bit magnitude comparison. A B  GT   (A>B) LT   (A<B) EQ    (A=B) 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 AB' A'B A'B' + AB= (A ⊙ B) The logic equations for the three output are: GT  =  AB’ LT   =  A’B EQ  = A’B' + AB = A  ⊙   B Figure-2: 1-bit magnitude comparator 2-bit Comparator This type of comparator is used to compare two numbers of 2-bits each. The table below shows the comparison. Functional table for two

Implementing with Decoders: A decoder is a combinational circuit that converts N-bit binary information to 2N unique output lines. It is able to represent upto 2N distinct elements of coded information. General type decoders usually come in sizes of Nx2N where N is the number of input lines. With a given input, only one of the 2N  output is active.   Applications of decoders: Decoders find numerous applications in : BCD to 7-segmanet decoders BCD to Decimal Decoder Memory address decoders Instruction decoders In Display devices 2 to 4 Line Decoder A 2 to 4 line decoder has 2 input lines, and 4 output lines. A decoder may also have an Enable (EN input) to enable or disable it. Enable Input Selection Lines Output Lines EN S1 S0 O0 O1 O2 O3 1 0 0 1       S1' S0' 0 0 0 1 0 1 0 1    S1' S0 0 0 1 1 0 0 0 1     S1 S0' 0 1 1 1 0 0 0 1      

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 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