logical registers

Registers*RegistersToday well see another common sequential device: registers.Theyre a good example of sequential analysis and design.They are also frequently used in building larger sequential circuits. Registers hold larger quantities of data than individual flip-flops.Registers are central to the design of modern processors.There are many different kinds of registers.Well show some applications of

these special registers.

Registers

Registers*What good are registers?Flip-flops are limited because they can store only one bit.We had to use two flip-flops for our two-bit counter examples.Most computers work with integers and single-precision floating-point numbers that are 32-bits long.A register is an extension of a flip-flop that can store multiple bits.Registers are commonly used as temporary storage in a processor.They are faster and more convenient than main memory.More registers can help speed up complex calculations.Well discuss RAM next time, and later well also see how registers are used in designing and programming CPUs.

Registers

Registers*A basic registerBasic registers are easy to build. We can store multiple bits just by putting a bunch of flip-flops together!A 4-bit register from LogicWorks, Reg-4, is on the right, and its internal implementation is below.This register uses D flip-flops, so its easy to store data without worrying about flip-flop input equations.All the flip-flops share a common CLK and CLR signal.

Registers

Registers*Adding a parallel load operationThe input D3-D0 is copied to the output Q3-Q0 on every clock cycle.How can we store the current value for more than one cycle?Lets add a load input signal LD to the register.If LD = 0, the register keeps its current contents.If LD = 1, the register stores a new value, taken from inputs D3-D0.

Registers

LD

Q(t+1)

0

Q(t)

1

D3-D0

Registers*Clock gatingWe could implement the load ability by playing games with the CLK input, as shown below.When LD = 0, the flip-flop C inputs are held at 1. There is no positive clock edge, so the flip-flops keep their current values.When LD = 1, the CLK input passes through the OR gate, so the flip-flops can receive a positive clock edge and can load a new value from the D3-D0 inputs.

Registers

Registers*Clock gating is badThis is called clock gating, since gates are added to the clock signal.There are timing problems similar to those of latches. Here, LD must be kept at 1 for the correct length of time (one clock cycle) and no longer.The clock is delayed a little bit by the OR gate.In more complex scenarios, different flip-flops in the system could receive the clock signal at slightly different times.This clock skew can lead to synchronization problems.

Registers

Registers*A better parallel loadAnother idea is to modify the flip-flop D inputs and not the clock signal.When LD = 0, the flip-flop inputs are Q3-Q0, so each flip-flop just keeps its current value.When LD = 1, the flip-flop inputs are D3-D0, and this new value is loaded into the register.

Registers

Registers*

A shift register shifts its output once every clock cycle.

SI is an input that supplies a new bit to shift into the register.For example, if on some positive clock edge we have:

SI = 1Q0-Q3 = 0110then the next state will be:Q0-Q3 = 1011The current Q3 (0 in this example) will be lost on the next cycle.

Shift registersQ0(t+1)= SIQ1(t+1)= Q0(t)Q2(t+1)= Q1(t)Q3(t+1)= Q2(t)

Registers

Registers*Shift direction

The circuit and example make it look like the register shifts right.

But it really depends on your interpretation of the bits. If you consider Q3 to be the most significant bit instead, then the register is shifting in the opposite direction!Q0(t+1)= SIQ1(t+1)= Q0(t)Q2(t+1)= Q1(t)Q3(t+1)= Q2(t)

Registers

Present Q0-Q3

SI

Next Q0-Q3

ABCD

X

XABC

Present Q3-Q0

SI

Next Q3-Q0

DCBA

X

CBAX

Registers*Shift registers with parallel loadWe can add a parallel load, just like we did for regular registers.When LD = 0, the flip-flop inputs will be SIQ0Q1Q2, so the register shifts on the next positive clock edge.When LD = 1, the flip-flop inputs are D0-D3, and a new value is loaded into the shift register, on the next positive clock edge.

Registers

Registers*Shift registers in LogicWorksHere is a block symbol for the Shift Reg-4 from LogicWorks. The implementation is shown on the previous page, except the LD input here is active-low instead.

Registers

i-clickerHow do you implement using the Shift Reg 4 the sequence 1, 3, 7, 15, 1, 3, that is, the sequence 0001, 0011, 0111, 1111, 0001, .

A) D0 =1, D1=1, D2=1, D3=1, SI=1, LD = 1

B) D0 =1, D1=0, D2=0, D3=0, SI=1, LD = 1

C) D0 =1, D1=0, D2=0, D3=0, SI=1, LD = Q3

D) D0 =1, D1=0, D2=0, D3=0, SI=0, LD = Q3

Registers*

Registers

Registers*Other types of shift registersLogical shifts Standard shifts like we just saw. In the absence of a SI input, 0 occupies the vacant position.Left: 0110 -> 1100Right: 0110 -> 0011Circular shifts (also called ring counters or rotates) The shifted out bit wraps around to the vacant position.Left: 1001 -> 0011Right: 1001 -> 1100Switch-tail ring counter (aka Johnson counter) Similar to the ring counter, but the serial input is the complement of the serial output.Left: 1001 -> 0010Right: 1001 -> 0100Arithmetical shifts Left shifting is the same as a logical shift. Right shifting however maintains the MSB.Left: 0110 -> 1100Right: 0110 -> 0011; 1011 -> 1101

Registers

i-clickerA switch-tail ring counter is similar to the ring counter, but the serial input is the complement of the serial output.List the sequence of states after each right shift until the register returns to 1001Register content 1001A) 0101, 1011, 1100, 0111, 1010, 0100, 0011, 1001

B) 1100, 0110, 0011, 1001

C) 0100, 1010, 1101, 0110, 1011, 0101, 0010, 1001

D) 1100, 0010, 0101, 1110, 0011, 1101, 1010, 1001

Registers*

Registers

Registers*Serial data transferOne application of shift registers is converting between serial data and parallel data.Computers typically work with multiple-bit quantities.ASCII text characters are 8 bits long.Integers, single-precision floating-point numbers, and screen pixels are up to 32 bits long.But sometimes its necessary to send or receive data serially, or one bit at a time. Some examples include:Input devices such as keyboards and mice.Output devices like printers.Any serial port, USB or Firewire device transfers data serially.Recent switch from Parallel ATA to Serial ATA in hard drives.

Registers

Registers*Receiving serial dataTo receive serial data using a shift register:The serial device is connected to the registers SI input.The shift register outputs Q3-Q0 are connected to the computer.The serial device transmits one bit of data per clock cycle.These bits go into the SI input of the shift register.After four clock cycles, the shift register will hold a four-bit word.The computer then reads all four bits at once from the Q3-Q0 outputs.

serial device

computer

Registers

Registers*Sending data seriallyTo send data serially with a shift register, you do the opposite:The CPU is connected to the registers D inputs.The shift output (Q3 in this case) is connected to the serial device.The computer first stores a four-bit word in the register, in one cycle.The serial device can then read the shift output.One bit appears on Q3 on each clock cycle.After four cycles, the entire four-bit word will have been sent.

serial device

computer

Registers

Registers*Registers in Modern Hardware Registers store data in the CPU Used to supply values to the ALU. Used to store the results. If we can use registers, why bother with RAM?

Answer: Registers are expensive! Registers occupy the most expensive space on a chip the core. L1 and L2 cache are very fast RAM but not

as fast as registers.Dunnington. Source INtel

Registers

Sheet1

CPUs

CPUGPR'sSizeL1 CacheL2 Cache

Pentium 4832 bits8 KB512 KB

Athlon XP832 bits64 KB512 KB

Athlon 641664 bits64 KB1024 KB

PowerPC 970 (G5)3264 bits64 KB512 KB

Itanium 212864 bits16 KB256 KB

MIPS R140003264 bits32 KB16 MB

Sheet2

Sheet3

Registers*Shift versus Multiply and DivideYou can multiply by powers of two by shifting to the leftA left shift by n is equivalent to multiplying by 2n

Example:3 * 2 = 6; 3*22 = 120011 1 = 0100; 1000 >> 2 = 0010; 0100 >> 1 = 0010; 1100 >> 1= 1110

-4 en twos complement-2 en twos complement

Registers

Registers*Why should I user shift instead of multiply?Program 1: Multiplication

#include ..

main() {scanf(%d,&mul);start = _rdtsc();for (i=0;i

Registers*Why should I user shift instead of integer division?Program 1: Division

#include ..

main() {scanf(%d,&mul);start = _rdtsc();for (i=0;i mul;}end = _rdtsc();printf("It took %llu cycles\n",end-start);return 0;}

Output: It took 912 cycles

Registers

Registers*Registers summaryA register is a special state machine that stores multiple bits of data.Several variations are possible:Parallel loading to store data into the register.Shifting the register contents either left or right.Counters are considered a type of register too!One application of shift registers is converting between serial and parallel data.Most programs need more storage space than registers provide.Well introduce RAM to address this problem.Registers are a central part of modern processors, as we will see in coming weeks.

Registers