Registers and Register Transfers¶

Registers, Microoperations and Implementations¶

Register: a collection of binary storage elements

In theory, a register is a sequential logic which can be defined by a state table。

2-bit Register

State table:

当位数增加时，状态表会变得非常大，因此需要一种更好的方式来描述寄存器。

设计寄存器的方法：

Add predefined combinational circuits to registers 给寄存器添加预定义的组合电路

Example: 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 将寄存器分解为单独的单元，然后将它们组合成寄存器

Register Storage and Load Enable¶

寄存器功能：

Load is a frequent name for the signal that controls register storage and loading
- Load = 1: Load the values on the data inputs
- Load = 0: Store the values in the register

需要实现数据保持，在 Load 信号控制下进行数据存储和加载。（低电平有效）

Solution:

Registers with Clock Gating

\(clk_G = \overline{Load} + clk\)

缺点：出现时钟歪斜。不应出现在同步电路中。
Registers with Load-Controlled Feedback

使用多路复用器实现 load 控制的数据保持。

Register Transfer Operations¶

The movement and processing of data stored in registers.

Three basic components:

set of registers
operations
control of operations

Elementary Operations: load, count, shift, add, bitwise "OR", etc, called microoperations.

Control of Operations: a set of signals that specify the microoperations to be performed and the registers in which they are to be performed. 控制哪些寄存器之间做什么操作。

Register Notations¶

Letters and numbers: 表示寄存器标识。
Parentheses(): 表示寄存器的某一位或某一区间的位，如 \(R_1(0)\)。
Arrow <-: 表示寄存器内容的传输，如 \(R_1 \leftarrow R_2\)。
Brackets [] – Specifies a memory address 表示内存地址。如 \(R_1 \leftarrow M[PC]\) 表示把 PC 命令的内存地址存储到 R1 中。

Conditional Transfer¶

K 控制传输的条件，当 K 为 1 时，传输发生。

Example

If (K1=1) then (\(R_2 \leftarrow R_1\)) 写成 K1: \(R_2 \leftarrow R_1\)。

即 K1 控制 R2 的接受，R1 的内容始终已经准备好，当 K1 为 1 时，R2 接受 R1 的内容。

Arithmetic Microoperations¶

Shift Microoperations:

Register Cell Design¶

Assume that a register consists of identical cells.

Each cell has:

a register
Data inputs to the register
Control input combinations to the register 控制信号
A set of register functions 对应每个控制信号的操作
A hold state specification 保持状态

Example

Register A (m-bits) Specification:

Data input: B
Control inputs (CX, CY)
Control input combinations (0,0), (0,1) (1,0)
Register transfers:
- CX: \(A \leftarrow B \vee A\)
- CY: \(A \leftarrow B \oplus A\)
Hold state: (0,0)
Load control: Load = CX + CY

Sequential Circuit Design Approach:

Find a state diagram or state table 现态、输入、控制信号共同决定次态。

续

State Table:

Register Transfer Structures¶

Multiplexer-Based Transfers¶

Multiplexers connected to register inputs produce flexible transfer structures.

Example

R0 load 信号为 \(K_1 + K_2 \overline{K_1} = K_1 + K_2\)

Multiplexer and Bus-Based Transfers for Multiple Registers¶

Dedicated MUX-Based Transfers

开销太大。
Multiplexer Bus

通过总线连接多个寄存器，通过控制总线的传输来控制寄存器的传输。

优点：灵活，开销小。
Three-State Bus

通过三态门控制总线的传输。

Shift Registers¶

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.

Counters¶

Counters are sequential circuits which "count" through a specific state sequence. They can count up, count down, or count through other fixed sequences.

Ripple Counters: 输入接在最低有效位上（LSB），后面每一位的 clk 接在上一位的进位输出上。不是同步电路。
Synchronous Counters: Logic is used to implement the desired state sequencing. 同步电路。

Ripple Counters¶

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。

Synchronous Counters¶

Note

使用与门信号链控制计数：

当低位全为 1 且使能信号为 1 时，高位求反。

当位数增加时候，使用 look ahead 简化电路：每隔若干位，将输出使用与门接在一起。

Other Counters¶

Down Counter: counts downward instead of upward
Up-Down Counter: counts up or down depending on value a control input such as Up/Down
Parallel Load Counter: Has parallel load of values available depending on control input such as Load
Modulo n Counter: n 进位计数器，当计数到 n 时，回到 0，重新开始计数。

Counter with Parallel Load¶

Modulo n Counter¶

使用异步清零实现：

缺点：会产生很短的脉冲，可能会导致错误。
使用同步清零实现：提前准备好清零。

自定义初值：

从 9 开始计数到 15。

Serial Transfers and Microoperations¶

寄存器一次只接受一个二进制位，可以使得时钟周期更短，但是传输相同位数的数据需要更多的时钟周期。

可以使用更简单的电路实现 microoperations: 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 Adder