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東京大学 情報理工学系研究科 創造情報学専攻 2012年8月実施 筆記試験 第2問

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Author​

itsuitsuki

Description​

Design a logic circuit to light an LED satisfying the following conditions. Figure 1 shows the connection diagram of the circuit, input signals and an output signal to the LED.

Condition 1: Inputs of the circuit to design are LEDSTR and CLOCK INPUT (100 kHz100\text{ kHz} clock input signal). The output of the circuit to design is LEDOUT. LEDOUT is directly connected to the LED driver and lights the LED. When LEDOUT is H, LED is on, and when LEDOUT is L, LED is off.

Condition 2: LEDSTR (INPUT 0, INPUT1, INPUT2) specifies the strength of the LED lighting. When LEDSTR is 0, the LED is completely turned off. When LEDSTR is 5, the LED is continuously turned on. When 1 <= LEDSTR <= 4, the strength of the light from the LED is proportional to the value of LEDSTR. When LEDSTR is more than or equal to 6, any behavior of the circuit is allowed.

Condition 3: When the LED turns on and off repeatedly at more than 100Hz100\text{Hz}, the strength of the LED light is seen as an average value of the time periods when the LED is turned on.

Condition 4: The logic circuit is designed using AND, OR, XOR, NOT and D-type Flip-Flops.

Design the circuit following the questions below.

  1. Design a 3-bit counter that count from 0 to 4 repeatedly such as 0→1→2→3→4→0→1……0\rightarrow1\rightarrow2\rightarrow3\rightarrow4\rightarrow0\rightarrow1\dots\dots

  2. Design a circuit that compares two 3-bit numbers.

  3. Design a circuit to turn on the LED for 1 clock period when LEDSTR is 1, 2 clock periods when LEDSTR is 2, ......., 5 clock periods (i.e. always on) when LEDSTR is 5. Figure 2 is an example of the output waveform.

  4. Using the logic circuit designed in (3), design a logic circuit that turns on and turns off the LED once for more than a second with the strength of the light specified by LEDSTR.

题目描述​

设计一个控制 LED 亮度的逻辑电路，连接与波形见原文图 1、2，并满足：

  • 输入为三位 LEDSTR（INPUT0, INPUT1, INPUT2）和频率 (100,\mathrm{kHz}) 的 CLOCK INPUT，输出为直接连接 LED 驱动器的 LEDOUT；LEDOUT=H 时点亮，LEDOUT=L 时熄灭。
  • LEDSTR 指定亮度：为 0 时完全熄灭，为 5 时持续点亮；在 (1\le\texttt{LEDSTR}\le4) 时，感知亮度与其数值成正比；大于等于 6 时电路行为不限。
  • LED 以高于 (100,\mathrm{Hz}) 的频率反复开关时，人眼感知亮度等于其点亮时间占比对应的平均值。
  • 只能使用 AND、OR、XOR、NOT 门和 D 触发器。

按以下步骤设计：

  1. 设计一个循环计数的 3 位计数器： [ 0\to1\to2\to3\to4\to0\to1\to\cdots. ]
  2. 设计比较两个 3 位数的电路。
  3. 设计 LED PWM 电路：LEDSTR 为 1 时每 5 个时钟点亮 1 个时钟周期，为 2 时点亮 2 个周期，依此类推；为 5 时点亮 5 个周期，即始终点亮。
  4. 利用第 3 问电路，再设计一个电路，使 LED 以 LEDSTR 指定的亮度点亮一次、熄灭一次，且每次点亮与熄灭均持续一秒以上。

考点​

  • 计数器与 D 触发器：由模 5 状态循环推导三位同步计数器的次态逻辑。
  • 三位比较器：从高位到低位组合相等与大小关系，产生比较结果。
  • 脉宽调制：比较模 5 计数值与亮度码，以占空比 (0/5) 至 (5/5) 控制 LED 平均亮度。
  • 多级分频：从 (100,\mathrm{kHz}) 时钟构造足够低频的计数链，使亮灭阶段各持续至少一秒。
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