## Digital Circuits/Registers and Counters

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Let's say we take several latches, and we put them all in a row. We can then connect the outputs of each latch to the inputs of the next latch in the following way: Each clock cycle, the output of one latch goes into the next latch, and the next latch receives the data. In this way, we essentially "shift" each value down the row of latches. This mechanism is called a shift register. Registers are groups of flip-flops FF binary storage and registers ppt, where each flip-flop FF is capable of storing one bit of information.

An n -bit register is a group of n flip-flops. The basic function of a register is to hold information in a digital system and make it available to the logic elements for the computing process. Registers consist of a finite number of flip-flops. Since each flip-flop is capable of storing either a "0" or a "1", there is a finite number of combinations that can be stored binary storage and registers ppt a register.

Each of those combinations is known as state or content of the register. With flip-flops we can store data bitwise but usually data does not appear as single bits.

Instead it is common to store data words of n bit with typical word lengths of 4, 8, 16, 32 or 64 bit. Thus, several flip-flops are combined to form a register to store whole data words.

Registers are synchronous circuits thus all flip-flops are controlled by a common clock line. As registers are often used to collect serial data they are also called accumulators. There exist several types of registers as there are. Information often comes bitwise i. Shift registers are used to store such data. A shift register has one serial input. Every clock pulse one bit is loaded from serial in into the first flip-flop of the register while all the actual flip-flop contents are shifted to the next flip-flop, dropping the last bit.

Shift registers may feature a serial output so that the last bit that gets shifted out of the register can be processed further. It is thus possible to build up a chain binary storage and registers ppt shift registers by connecting each serial out to another shift register's serial in, effectively creating a single big shift register.

It is also possible to create a Cyclic register see next paragraph by connecting the serial out to the same register's serial in. Shift register circuits may also feature additional parallel-in functionality that allows manipulation of individual bits. A typical purpose for such a SIPO register is to collect data binary storage and registers ppt is delivered bitwise and that is needed in n-bit data words e.

Shifting bits are important for mathematical operations: Thus the bit that usually would get dropped is fed to the register input again to receive a cyclic serial register. As there is a need for serial — parallel conversion the inverse operation is equally required.

For this operation it needs two control lines: A barrel shifter is a digital circuit that can shift a data word by a specified number of bits in one clock cycle.

It can be implemented as a sequence of multiplexers mux. For example, take a 4-bit barrel shifter, with inputs A, B, C and D. Binary storage and registers ppt is, binary storage and registers ppt can shift all of the outputs up to three positions to the right and thus make any cyclic combination of A, B, C and D. The barrel shifter has a variety of applications, including being a useful component in microprocessors alongside the ALU.

A common usage of a barrel shifter is in the hardware implementation of floating-point arithmetic. For a floating-point add or subtract operation, the significand of the two numbers must be aligned, which requires shifting the smaller number to the right, increasing its exponent, until it matches the exponent of the larger number. This is done by subtracting the exponents, and using the barrel shifter to shift the smaller number to the right by the difference, in one cycle.

If a simple shifter were used, shifting by n bit positions would require n clock cycles. Cascade shifters are circuits that switch contents of each serial in parallel out register be means of a decoder. A counter is a sequential circuit that — counts. That means it proceeds through a pre-defined sequence of states where the state of the circuit is determined by the states of all binary storage and registers ppt flip flops.

As every state of the circuit can be a given number, we can say that a counter produces a binary storage and registers ppt of numbers. Binary storage and registers ppt most basic counters will simply increment by 1 with every clock pulse, so after state it will go to ; the next pulse will let it switch to etc. It is possible to design counters with any needed counting sequence. Even though asynchronous sequential circuits are not subject of this course the asynchronous counter is presented here exceptionally to give a slight impression.

For these counters an external clock signal is applied to one flip-flop, and then the output of the preceding flip-flop is connected to the clock of the next flip-flop. The clock is applied to first flip flop. The clock is applied to the first Binary storage and registers ppt in the series, binary storage and registers ppt the T input is set to 1. This effectively halves the clock input to the second FF and causes it to toggle whenever the preceding FF hits 0 after 1.

This is known as the ripple action, that is, the toggle ripples across all subsequent FFs, effectively giving rise to what we know as the counting binary storage and registers ppt. A beautiful example demonstrating this functionality can be found here.

In synchronous counter all the flip flops receive the external clock pulse simultaneously. Ring counter and Johnson counter are the examples of synchronous counters.

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