A sequential circuit has one input X and four outputs Z₁ Z₂ Z3 Z4. Z₁ Z2 Z3 Z4 represents the gray code encoded number equal to the number of pairs of adjacent 1's that have been received as inputs. Use the gray code that is on page 22 of the textbook. For example, if the circuit had received 7 pairs of 1's as inputs, Z₁ Z2 Z3 Z4 = 1011. In addition, the circuit resets when the circuit receives 5 pairs of 1's. Find a Moore state graph and table for the circuit.

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### Sequential Circuit Analysis with Gray Code Encoding

A sequential circuit has one input \( X \) and four outputs \( Z_1Z_2Z_3Z_4 \). The output \( Z_1Z_2Z_3Z_4 \) represents the gray code encoded number equal to the number of pairs of adjacent 1's that have been received as inputs. Use the gray code that is on page 22 of the textbook. For example, if the circuit had received 7 pairs of 1's as inputs, \( Z_1Z_2Z_3Z_4 = 1011 \). In addition, the circuit resets when it receives 5 pairs of 1's. Find a Moore state graph and table for the circuit.

#### Examples:
1. **Input sequence:**
   \[
   X = 1 \ 0 \ 1 \ 1 \ 1 \ 0 \ 0 \ 1 \ 1 \ 0 \ 1 \ 1 \ 0 \ 1 \ 0 \ 1 \ 1 \ 0
   \]
   **Output sequences:**
   \[
   Z_1 = 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 1 \ 0 \ 0
   \]
   \[
   Z_2 = 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0
   \]
   \[
   Z_3 = 0 \ 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0
   \]
   \[
   Z_4 = 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0
   \]

2. **Input
Transcribed Image Text:### Sequential Circuit Analysis with Gray Code Encoding A sequential circuit has one input \( X \) and four outputs \( Z_1Z_2Z_3Z_4 \). The output \( Z_1Z_2Z_3Z_4 \) represents the gray code encoded number equal to the number of pairs of adjacent 1's that have been received as inputs. Use the gray code that is on page 22 of the textbook. For example, if the circuit had received 7 pairs of 1's as inputs, \( Z_1Z_2Z_3Z_4 = 1011 \). In addition, the circuit resets when it receives 5 pairs of 1's. Find a Moore state graph and table for the circuit. #### Examples: 1. **Input sequence:** \[ X = 1 \ 0 \ 1 \ 1 \ 1 \ 0 \ 0 \ 1 \ 1 \ 0 \ 1 \ 1 \ 0 \ 1 \ 0 \ 1 \ 1 \ 0 \] **Output sequences:** \[ Z_1 = 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 1 \ 0 \ 0 \] \[ Z_2 = 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0 \] \[ Z_3 = 0 \ 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0 \] \[ Z_4 = 0 \ 0 \ 1 \ 1 \ 1 \ 1 \ 1 \ 1 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \ 0 \] 2. **Input
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