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Register and Register Transfers

Abstract

  1. 寄存器的概念、设计模型和结构
    Register, Register Design Models

    • 门控时钟、并行加载控制
      Registers with Clock Gating, Registers with Load-Controlled Feedback

  2. 寄存器传输操作基本概念
    Register transfer operations

    • 寄存器传输语言、基本微操作、条件传输原理、多寄存器传输的三种基本结构、原理和优缺点
      Register Transfer Language (RTL), Microoperations, conditional transfer, three types of Register Transfer Structures: Multiplexer-Based Transfers, Bus-Based Transfers, Three-State Bus
    • RTL与硬件描述语言的关系
      Relationship of RTL and Verilog, implementation of conditional operations

  3. 移位寄存器的概念、结构
    Shift Registers

    • 串行输入、左移、右移、并行加载
      serial input, shift left, shift right, parallel load

  4. 计数器的功能、类型
    Function and type of counters

    • 纹波计数器的结构、工作原理、优缺点
      Structure, theory, characteristic of ripple counter
    • 同步计数器的结构、工作原理、优缺点
      Structure, theory, characteristic of synchronous counter
    • 进位链、并行进位、并行加载
      carry chain, parallel carry, parallel load

  5. 采用同步时序电路设计方法设计模n计数器
    Use the sequential logic model to designmodulo n counters

  6. 采用输出结果反馈的方法设计模n计数器
    Use output feedback model to design modulo n counters

  7. 寄存器设计
    RegisterDesign

    • 基于寄存器单元的设计方法，采用多路复用器设计
      RegisterCellDesign,Multiplexer Approach
    • 基于时序电路设计方法的寄存器设计
      Sequential Circuit Design Approach

  8. 串行传输和微操作
    Serial Transfers and Microoperations

Registers

Register – a collection of binary storage elements

In theory, a register is a sequential logic which can be defined by a state table. More often, think of a register as storing a vector of binary values.

Example

如果有 \(n\) 位寄存器，需要 \(2^n\) 状态. \(n\) 可能会很大，导致需要的状态，可能的输入组合、输出函数会很大。

Due to the large numbers of states and input combinations as n becomes large, the state diagram/state table model is not feasible!

  • Add predefined combinational circuits to registers(e.g. To count up, connect the register flip-flops to an incrementer)
  • Design individual cells using the state diagram/state table model and combine them into a register
    把寄存器拆成单位的来设计，再考虑多位的拼接，最后组成多位寄存器。

Register Storage and Load Enable

Expectations:

  • A register can store information for multiple clock cycles
  • To “store” or “load” information should be controlled by a signal

但在刚刚的例子中，每个周期都会保存新的数据，不能做到在多个周期保留数据，因此是不行的。

Realizing expectations:

  • Use a signal to block the clock to the register
  • Use a signal to control feedback of the output of the register back to its inputs
  • Use other SR or JK flip-flops, that for (0,0) applied, store their state

Load is a frequent name for the signal that controls register storage and loading

  • Load = 1: Load the values on the data inputs(加载外部新数据)
  • Load = 0: Store the values in the register(保持原有的数据)

Solution

  • Registers with Clock Gating
    The \(\overline{Load}\)(bar 表示低电平有效) signal enables the clock signal to pass through if 0 and prevents the clock signal from passing through if 1. (与 \(Load\) 相反)

    Example

    For Positive Edge-Triggered or Negative Pulse Master-Slave Flip-flop:

    \(Gated\ Clock = Clock + \overline{Load}\) 当 \(\overline{Load}\) 信号为 1 时，时钟信号不再随着外部时钟改变，这时就是保持原有的数据。

    Clock Skew
    问题在于我们是同步时序电路实现，要求时钟统一提供，这样所有的触发器会在同一时间完成操作。使用门控时钟的方式会带来更多的触发时间，时序电路从同步变为了异步的时序电路（触发有前有后）

  • Registers with Load-Controlled Feedback
    Run the clock continuously, and Selectively use a load control to change the register contents.

    Example

Register Transfer Operations

  • Register Transfer Operations – The movement and processing of data stored in registers

  • Three basic components:

    • set of registers(源寄存器，目标寄存器)
    • operations
    • control of operations
  • Elementary Operations -- load, count, shift, add, bitwise "OR", etc.
    Elementary operations called microoperations

Register Notation

  • Letters and numbers – denotes a register (e.g. \(R2, PC, IR\))
  • Parentheses \((\ )\) – denotes a range of register bits (e.g. \(R1(1), PC(7:0), PC(L)\))
  • Arrow \((\leftarrow)\) – denotes data transfer (e.g. \(R1 \leftarrow R2, PC(L) \leftarrow R0\)) H 代表高位, L 代表低位(如 \(PC(L),PC(H)\) 分别代表 \(PC\) 的高八位和低八位)
  • Comma – separates parallel operations
  • Brackets \([\ ]\) – Specifies a memory address (e.g. \(R0 \leftarrow M[AR], R3 \leftarrow M[PC]\)) 寻址
Conditional Transfer

如果 \(K1=1\) 那么将 \(R1\) 的信号传给 \(R2\), 我们可以写为 \(K1:(R2\leftarrow R1)\), 其中 \(R1\) 是一个控制变量，表明条件执行的发生是否发生。

Register Cell Design

Assume that a register consists of identical cells.(每个位执行相同操作)

  • Design representative cell for the register
  • Connect copies of the cell together to form the register
  • Applying appropriate "boundary conditions" to cells that need to be different and contract if appropriate

Specifications

  • A register
  • Data inputs to the register
  • Control input combinations to the register
    e.g. 控制输入: Load, Shift, Add. 我们可以用三个引脚分别表示控制输入(not encoded, one-hot code)，也可以用两个引脚 S0 S1 的组合来表示控制输入(encoded)
  • A set of register functions (typically specified as register transfers) 即规定控制输入的函数是对数据进行什么样的操作
  • A hold state specification(e.g. If all control inputs are 0, hold the current register state)

Design

设计时，除了 Multiplexer Approach 还有 Sequential Circuit Design Approach

  • Find a state diagram or state table
  • Use the design procedure in Chapter 4 to complete the cell design
  • For optimization:
    • Use K-maps for up to 4 to 6 variables
    • Otherwise, use computer-aided or manual optimization

Microoperations

Logical Groupings:

  • Transfer - move data from one register to another
  • Arithmetic - perform arithmetic on data in registers \(+-\times /\)
  • Logic - manipulate data or use bitwise logical operations \(\wedge \vee \oplus \ \overline{x}\)
  • Shift - shift data in registers
+

"+" 在逻辑表达式中表示或，在算术表达式中表示加法。
如 \((K1 + K2): R1 \leftarrow R1 +R3\), 左边为或，右边为加。

RTL, VHDL, Verilog Symbols for Register Transfers

Arithmetic Microoperations

  • Note that any register may be specified for source 1, source 2, or destination.
  • These simple microoperations operate on the whole word

Logical Microoperations

Shift Microoperations

These shifts "zero fill". Sometimes a separate flip-flop is used to provide the data shifted in, or to “catch” the data shifted out.

Other shifts are possible (rotates, arithmetic).

Example

假设 \(R2=1100\ 1001\)

  • \(R1 \leftarrow sl\ R2\) 之后 \(R2=1001\ 0010\)
  • \(R1 \leftarrow sr\ R2\) 之后 \(R2=0110\ 0100\)

Register Transfer Structures

  • Multiplexer-Based Transfers - Multiple inputs are selected by a multiplexer dedicated to the register
  • Bus-Based Transfers - Multiple inputs are selected by a shared multiplexer driving a bus that feeds inputs to multiple registers
  • Three-State Bus - Multiple inputs are selected by 3-state drivers with outputs connected to a bus that feeds multiple registers
  • Other Transfer Structures - Use multiple multiplexers, multiple buses, and combinations of all the above

Multiplexer-Based Transfers

Multiplexers connected to register inputs produce flexible transfer structures (Note: Clocks are omitted for clarity)

Example

\(K1:R0\leftarrow R1\quad K2\overline{K1}:R0\leftarrow R2\)
我们可以将其化简: \(K1+K2\overline{K1}=K1+K2\) 就是 \(R0\) 寄存器会被更新时的控制逻辑. 并用 \(K1\) 作为 Mux 的选择信号。

完整电路（假设寄存器均为 4 位）

Multiplexer and Bus-Based Transfers for Multiple Registers

  • Multiplexer dedicated to each register

    There can be three distinct registers as source, so can simultaneously do any three register transfers. (totally flexible)
    如我们可以既可以实现 \(R0\leftarrow R1\) 也可以实现 \(R0\leftrightarrow R1\)
    电路成本太高！

  • Shared transfer paths for registers
    A shared transfer object is a called a bus(总线)

    A single bus driven by a multiplexer lowers cost, but limits the available transfers
    不能同时 \(R0\leftarrow R1\) \(R1\leftarrow R0\)(类比：交换函数需要一个第三方变量)

Three-State Bus

Same simultaneous transfer capability as multiplexer bus
我们将寄存器和三态门封装在一起考虑，那么我们只需要一个外部引脚(n bits), 但多路复用器的方法需要两根位宽是 n 的引脚（因为三态门的外部引脚是可以双向传输数据的）

Shift Registers

Shift Registers move data laterally within the register toward its MSB or LSB position

In the simplest case, the shift register is simply a set of D flip-flops connected in a row like this:

  • Data input, In, is called a serial input or the shift right input.
  • Data output, Out, is often called the serial output.

  • The vector (A, B, C, Out) is called the parallel output.

  • Parallel Load Shift Registers
    By adding a mux between each shift register stage, data can be shifted or loaded

    If SHIFT is low,\(D_A\) and \(D_B\) are replaced by the data on DA and DB lines, else data shifts right on each clock.
    缺点: 没有数据保持操作，需要多添加一个选择项(3-1 选择)

Counters

Counters are sequential circuits which "count" through a specific state sequence. They can count up, count down, or count through other fixed sequences. Two distinct types are in common usage:

  • Ripple Counters
    • Clock connected to the flip-flop clock input on the LSB bit flip-flop
    • For all other bits, a flip-flop output is connected to the clock input, thus circuit is not truly synchronous!
    • Output change is delayed more for each bit toward the MSB.
    • Resurgent because of low power consumption
  • Synchronous Counters
    • Clock is directly connected to the flip-flop clock inputs
    • Logic is used to implement the desired state sequencing

Ripple Counter

每个时钟周期，A 计数器翻转一次。当 A 处于下降沿的时候 B 会进行一次求反。

每个触发器的时钟，没有接在同一个系统时钟上，是一个异步时序电路。

Question

考虑 3 位触发器，理想上 \(C=B=A=1\) 后从全 1 立即变成全 0. 但因为门延迟，实际变化过程为\(111-110-100-000\)

此外对于 \(n\) bits, 最坏时间延迟是 \(n\cdot t_{PHL}\), 速度会非常慢

Synchronous Counters

up-counter: incrementer \(S=A+1\)

当位数增加，不利于化简设计。观察 \(Q_2\), 我们发现每次翻转的时候 \(Q_1,Q_0\) 均为 1. 类似在二进制计数器中 \(Q_n\) 只有在低 \(n-1\) 位均为 1 时才会取反。
我们可以用异或门，接在控制引脚和本位输出上，利用控制引脚来实现对本位输出的保持/取反。

这里的控制信号是一个与门链，Count Enable 是与门链的使能。（若 Enable 为 0, 所有的与门链均为 0, 这时电路相当于是保持功能）
最后与门链输出一个 Carry Output, 表示所有位为 1 且 Enable=1. CO 是用于做级联（如两个四位计数器拼成一个八位计数器）接在后续计数器的 Enable 上。

存在问题：与门链是串接的，当计数器位数大时，与门链的传输延迟可能会影响计数器。
parallel gating:

Symbol for Synchronous Counter

Other Counters - Counter with Parallel Load

在 D 输入触发器前加上 2-1 Mux(Load 是选择信号), 选择与门链的结果(Load=0) or 外部输入(Load=1)，可以实现并行加载和计数的选择控制

Load Count Action
0 0 Hold Stored Value
0 1 Count Up Stored Value
1 X Load D
Design Example: Synchronous BCD

利用时序电路实现同步 BCD 计数器

  • 状态表如下:(1010-1111 don't cares)

  • 基于上面的状态表，分别对 \(Q8,Q4,Q2,Q1\) 画卡诺图
    利用卡诺图两级优化

\[ \begin{align*} D1 & = \overline {Q1}\\ D2 & = Q2 \oplus Q1\overline{Q8}\\ D4 & = Q4 \oplus Q1Q2\\ D8 & = Q8 \oplus (Q1Q8 + Q1Q2Q4) \end{align*} \]
  • 画出电路图，添加复位引脚(reset)
    可以增加在触发器输入端(synchronous); 或者直接接在 D 触发器的异步复位 R 一端(asynchronous)
  • 如果电路因为干扰，跳到了无关态，能否恢复 ?
    画出无关态的次态

可以看到不会跳到异常状态后进入死锁，画出状态图如下

Other Counters - Counting Modulo N

BCD 码计数器就是模 10 计数器。 常用做法是将二进制计数器进行功能转换，利用同步/异步清零，加载功能，达到 \(N\) 时中止计数结果

  • 检测值到达 N 后直接用异步清零引脚将计数器清零

    Counting Modulo 7: Detect 7 and Asynchronously Clear

    • A synchronous 4-bit binary counter with an asynchronous \(Clear\)(异步复位脚，后同) is used to make a Modulo 7 counter.
    • Use the \(\overline{Clear}\) feature to detect the count 7 and clear the count to 0. This gives a count of 0, 1, 2, 3, 4, 5, 6, 7(short)0, 1, 2, 3, 4, 5, 6, 7(short)0, etc.
      但会短暂出现 7 这个状态，可能会带来干扰
    • 检测值达到 \(N-1\) 时利用同步清零的方式在下个周期上升沿将计数器清零

    Counting Modulo 7: Synchronously Load on Terminal Count of 6

    • A synchronous 4-bit binary counter with a synchronous load and an asynchronous \(Clear\) is used to make a Modulo 7 counter
    • Use the Load feature to detect the count "6" and load in "zero". This gives a count of 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, ...
      不会直接清零，而是在到达 \(N-1\) 的时候，在下个时钟上升沿将其清零

    如果需要设计从某个中间值(非零)开始计数的计数器，只需要将每次复位赋的外部输入变为该数字即可(如果是 mod 15, 可以不需要用与门，直接利用之前的 Carry Output 即可)

多位计数器

多位寄存器，分开设计，如设计时间，低位为模 10 计数器，高位为模 6 计时器，低位的 Carry Output 既作为低位的同步清零信号，又是高位的 Enable 信号.

Serial Operations

串行：
寄存器一次只接受一个二进制位，如果传输 n 位需要 n 个时钟周期。

需要的引线数量少，两个设备之间只需要一条线和一条地线就可以了。而且因为引线少，我们可以让其时钟频率达到非常高。

e.g. 设备与设备之间常使用串行(外设), USB, 以太网线

By using two shift registers for operands, a full adder, and a flip flop (for the carry), we can add two numbers serially, starting at the least significant bit.

Serial addition is a low cost way to add large numbers of operands, since a “tree” of full adder cells can be made to any depth, and each new level doubles the number of operands.

Other operations can be performed serially as well, such as parity generation/checking or more complex error-check codes.

Serial Adder

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