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Line coding 1101010111 (polar NRZ, polar RZ, Manchester, AMI)

Short answer

For 1101010111: Polar NRZ: 1→+V, 0→-V full bit. Polar RZ: 1→+V half-bit then 0, 0→-V half-bit then 0. Manchester: 1→+V then -V, 0→-V then +V. AMI: 0→0 V, 1s alternate +V,-V starting +V. Each code format described.

Given the binary sequence 1101010111 represent in polar NRZ, polar RZ, Manchester and AMI codes.

Line codes convert the bit stream into electrical pulses. Conventions used (bit period TbT_b, amplitude VV):

  • Polar NRZ: 1 → +V+V, 0 → −V-V for the full bit.
  • Polar RZ: 1 → +V+V, 0 → −V-V for the first half bit, then 0.
  • Manchester: 1 → +V+V then −V-V (high-to-low at mid-bit); 0 → −V-V then +V+V.
  • AMI: 0 → 0 V; successive 1s alternate +V+V, −V-V (first 1 taken as +V+V, full-width pulses).

Bit sequence: 1 1 0 1 0 1 0 1 1 1

bits  1   1   0   1   0   1   0   1   1   1  

Polar NRZ:
+V  |‾‾‾‾‾‾‾‾    ‾‾‾‾    ‾‾‾‾    ‾‾‾‾‾‾‾‾‾‾‾‾
 0  |
-V  |        ____    ____    ____

Polar RZ:
+V  |‾‾  ‾‾      ‾‾      ‾‾      ‾‾  ‾‾  ‾‾
 0  |  --  --  --  --  --  --  --  --  --  --
-V  |        __      __      __

Manchester:
+V  |‾‾  ‾‾    ‾‾‾‾    ‾‾‾‾    ‾‾‾‾  ‾‾  ‾‾
 0  |
-V  |  __  ____    ____    ____    __  __  __

AMI (bipolar NRZ):
+V  |‾‾‾‾        ‾‾‾‾            ‾‾‾‾    ‾‾‾‾
 0  |        ----    ----    ----
-V  |    ____            ____        ____

Level in each bit (a pair means first half, second half):

Code1101010111
Polar NRZ+V+V−V+V−V+V−V+V+V+V
Polar RZ+V,0+V,0−V,0+V,0−V,0+V,0−V,0+V,0+V,0+V,0
Manchester+V,−V+V,−V−V,+V+V,−V−V,+V+V,−V−V,+V+V,−V+V,−V+V,−V
AMI (bipolar NRZ)+V−V0+V0−V0+V−V+V

Observations: polar NRZ has a DC component when 1s are more frequent (here seven 1s); Manchester has a transition in every bit, so it carries timing; AMI has zero average value because its marks alternate.

✓ Answer checked by Claude Opus 5.5 (high effort)

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