A sequence detector is designed to detect precisely 3 digital inputs, with overlapping sequences detectable. For the sequence (1,0,1) and input data (1,1,0,1,0,0,1,1,0,1,0,1,1,0), what is the output of this detector?

The correct answer option is 0,1,0,0,0,0,0,1,0,1,0,0.

A sequence detector for the target sequence (1, 0, 1) checks every continuous 3-bit window of the incoming digital input stream. Since overlapping sequences are detectable, the 3-bit window advances by one bit position for each clock cycle once the initial 3 bits have been received.

Given the input data sequence:
Input: (1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0)

We evaluate the output after receiving at least 3 bits to form a valid 3-bit pattern:

1. Bits 1 to 3: (1, 1, 0) ⇒ Output = 0
2. Bits 2 to 4: (1, 0, 1) ⇒ Output = 1 (Sequence detected!)
3. Bits 3 to 5: (0, 1, 0) ⇒ Output = 0
4. Bits 4 to 6: (1, 0, 0) ⇒ Output = 0
5. Bits 5 to 7: (0, 0, 1) ⇒ Output = 0
6. Bits 6 to 8: (0, 1, 1) ⇒ Output = 0
7. Bits 7 to 9: (1, 1, 0) ⇒ Output = 0
8. Bits 8 to 10: (1, 0, 1) ⇒ Output = 1 (Sequence detected!)
9. Bits 9 to 11: (0, 1, 0) ⇒ Output = 0
10. Bits 10 to 12: (1, 0, 1) ⇒ Output = 1 (Sequence detected with overlap!)
11. Bits 11 to 13: (0, 1, 1) ⇒ Output = 0
12. Bits 12 to 14: (1, 1, 0) ⇒ Output = 0

Combining the outputs starting from the 3rd input bit yields the sequence:
$0,1,0,0,0,0,0,1,0,1,0,0$