Complements are used in digital computers for facilitating the subtraction operation and for logical manipulation. There are two methods of complements for each base r system: the r's complement and the (r - 1)'s complement.(r - 1)'s Complement9's complementGiven a number N in base r having n digits, the (rn - 1)'s complement of N is represented as (rn- 1) - N. For decimal numbers r = 10 and r - 1 = 9, therefore the 9's complement of N is (10n - 1) - N.Now, 10n defines a number that includes a single 1 followed by n 0's. 10n ... Read More

A digital circuit that executes the inverse services of a decoder is known as an encoder. It has 2ninput lines and n output lines. In an encoder, the output lines create the binary code equivalent to the input value. The diagram shows the general architecture of an encoder circuit.Decimal to BCD EncoderThe decimal to BCD encoder has ten input lines and four output lines. The input for the encoder is the decoded decimal data and encoded BCD is the output accessible on the four output lines. The diagram demonstrates the logic symbol for decimal to BCD encoder IC.The diagram demonstrates ... Read More

A binary decoder is a decoder that has an n-bit binary input code and one activated output which is chosen from output codes. This decoder is accessible in instances where it is important to simulate directly one of the outputs based on an n-bit input value. In a 2 to 4 decoder, 2 inputs are decoded into four outputs, each output describing one of the min-terms of the 2 input variables. The two inverters support the complement of the inputs and each one of the four AND gates creates one of the min-terms.The diagram shows the circuit diagram of a ... Read More

A circuit that makes data on an individual line and sends the data on any of the 2 n possible output lines is known as a demultiplexer. Hence, a demultiplexer is known as a single-input multiple-output switch. The values of n selection lines control the selection of a determined output line.A demultiplexer is demonstrated in the diagram.The truth table of a demultiplexer circuit is demonstrated in the table.EnableS1S0DinY0Y1Y2Y30XXX0000100000001001100010100001011010011110000110100101110000011110001A demultiplexer is used extensively in clock demultiplexer, security monitoring system, synchronous data transmission system, etc.Application of DeMultiplexerDemultiplexer can link a single source to various destinations. The principal application field of demultiplexer is ... Read More

A multiplexer is a combinational circuit that obtains binary data from one of 2" input data lines and manages it to an individual output line. The selection of a specific input data line for the output is decided by a collection of selection inputs. A 2"-to-1 multiplexer has 2" input data lines and n input selection lines whose bit combinations decide which input data are chosen for the output.A 4-to-1-line multiplexer is demonstrated in the figure. Each of the four data inputs I0 through I3 is used to one input of an AND gate. The two selection inputs S1 and ... Read More

A register that goes through a fixed series of states upon the software of input pulses is known as a counter. The input pulses can be clock pulses or can emerge from an outside source. They can appear at orderly intervals of time or at random.Counters are initiate in almost all apparatus including digital logic. It can be used for counting the multiple occurrences of an event and are beneficial for producing timing signals to regulate the sequence of operations in digital computers. There are multiple sequences that a counter can follow and the consecutive binary sequence is clean and ... Read More

A register adequate for changing its binary data in one or both directions is known as a shift register. The logical design of a shift register includes a series of flip-flops, with the output of one flip-flop linked to the input of the next flip-flop.Operations of Shift RegisterThere are various modes of operations of shift registers which are as follows −Serial-In Serial-Out Shift RegisterThe controlling of shifting of information decides the ‘serial-in serial-out’ shift register into the right shift and left shift register. The diagram demonstrates a ‘serial-in serial-out’ right shift register.During the first clock pulse, the signal on the ... Read More

A register is a set of flip-flops with each flip-flop adequate for saving one bit of data. An n-bit register has a set of n flip-flops and is adequate for saving any binary data of n bits. In the flip-flops, a register can have combinational gates that implement specific data-processing operations.A register includes a set of flip-flops and gates that influence their change. The flip-flops manage the binary data and the gates control when and how current data is moved into the register.There are multiple kinds of registers that are accessible economically. The elementary register includes just flip-flops, with no ... Read More

The T flip-flop is also called toggle flip-flop. It is a change of the JK flip-flop. The T flip flop is received by relating both inputs of a JK flip-flop. The T flip-flop is received by relating the inputs ‘J’ and ‘K’. When T = 0, both AND gates are disabled. Therefore, there is no change in the output. When T= 1, the output toggles.The diagram demonstrates the circuit diagram of a T flip-flop.The truth table of T flip-flop is displayed in the table.QNTQN+1000011101110The logic symbol of the T flip-flop is shown in the figure.

The D flip-flop is a clocked flip-flop with a single digital input 'D'. Each time a D flip-flop is clocked, its output follows the state of 'D'. The D Flip Flop has only two inputs D and CP. The D inputs go precisely to the S input and its complement is used to the R input.Considering the pulse input is at 0, the outputs of gates 3 and 4 are at the 1 level and the circuit cannot convert state regardless of the value of D. The D input is sampled when CP = 1. If D is 1, the ... Read More