Shift registers and Floating Point Numbers Chapter 11 in Tokheim PHY 201 (Blum)

What are they? Recall that a register is a small piece of memory that holds values. In addition to holding values, a shift register performs a simple operation on the values; it moves them to the left or to the right. PHY 201 (Blum)

Example Serial output Serial input Shift register 1 PHY 201 (Blum)

Parallel loading register PHY 201 (Blum)

Register On the previous slide, the input of a flip-flop is selected from two possible choices The output of the same flip-flop The data switch above Recall that selecting from one of two inputs is done by a 2-to-1 MUX. The load line serves as the address/select input. PHY 201 (Blum)

When Load is high, we are selecting the data switches to be the data input. So when we go through a positive edge of the clock, we are writing the value from the data switches to the register. PHY 201 (Blum)

When Load is low, we are selecting the flip-flop’s output to be the data input. So when we go through a positive clock edge, we are writing the value from the flip-flop to the flip-flop – thus keeping the value the same as before (holding). PHY 201 (Blum)

Register  Shift Register We can adapt the previous circuit to make a shift register. Instead of having one of the two possible inputs for a flip-flop come from the output of the same flip-flop, we can change this to having that input come from an adjacent flip-flop. Then if when the load input is low and we go through a positive clock edge, the effect is not to hold the values of the register but to shift them. This is part of the lab. PHY 201 (Blum)

On the ends If one shifts from the right to the left, then the input to the rightmost flip-flop does not come from an adjacent flip-flop during the shift operation. There are several options Data switch input Always 1 Always 0 Use leftmost output to form a ring PHY 201 (Blum)

How are shift registers used? Modems Cyclic Redundancy Check (CRC) Multiplication Adding floats PHY 201 (Blum)

Modems A modem (Modulator-Demodulator) takes a signal from a computer and places it on a transmission line. A transmitting modem modulates, that is, converts a digital signal from a computer to a pseudo-analog signal more appropriate for a transmission line. The receiving modem demodulates, that is, converts the pseudo-analog signal back into digital form. PHY 201 (Blum)

Modems (Cont.) But the aspect of modems relevant here is that The transmitting modem converts parallel data to serial. The receiving modem converts serial data into parallel form. Inside the computer, data that moves around as words on parallel cables having a connection for each bit in the word. The transmission lines are longer and require data to be sent serially (one bit at a time). PHY 201 (Blum)

Parallel to Serial To leave the computer, data moves into register in parallel, several bits at once. Data then moves out of the register serially, one bit at a time. 1 PHY 201 (Blum)

Serial to Parallel 1 DEMO! To enter the computer, data enters the register in serial, one bit at a time. Data then moves out of the register in parallel. DEMO! PHY 201 (Blum)

Cyclic Redundancy Check In order to check for errors that may occur during transmission, the sender calculates a number, a cyclic redundancy check. The receiver does the same calculation. If they agree, then presumably no error occurred in transmission. Actually the receiver does a calculation that includes the sender’s CRC as part of the data and should get an answer of zero. It’s easier electronically to see if series of bits corresponds to zero. PHY 201 (Blum)

CRC Any mathematical operation performed on the transmitted data could serve as a check. Another common calculation is summing, then it is called a checksum. The calculation should not be time consuming. Think of CRC as a funny kind of division, the remainder from the division is the check. It’s not ordinary division, but a strange kind of division that is easy to realize electronically. PHY 201 (Blum)

CRC = Shift register + XORs Basically one has a shift register with a few excluded OR gates inserted in strategic positions. PHY 201 (Blum)

  11000001010   1 1 0001010   1 001010   1 01010 PHY 201 (Blum)

  1 1010   1 1 010   1 1 1 10   1 1 1   1 1 PHY 201 (Blum)

Multiplication: Shift and add 1  + shift shift PHY 201 (Blum)