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Line coding 100111010 (Polar RZ, bipolar NRZ, AMI, Manchester)

Short answer

Polar RZ sends +V half bit for 1, -V half bit for 0. Bipolar NRZ and AMI both alternate polarity on each 1, with full-width (NRZ) or half-width (RZ) pulses; 0 is no pulse. Manchester: 1=+V/-V, 0=-V/+V mid-bit transition.

Represent 100111010 using following encoders. a) Polar RZ b) Bipolar NRZ c) AMI d) Manchester

Bit sequence: 1 0 0 1 1 1 0 1 0, bit period TbT_b, levels ±V\pm V. The first 1 is taken as positive for the bipolar codes. Bipolar NRZ uses full-width pulses whose polarity alternates for each 1. AMI uses the same alternation with half-width (RZ) pulses.

a) Polar RZ

1 → +V for half the bit, 0 → −V for half the bit, then return to 0.

Polar RZ

    1   0   0   1   1   1   0   1   0  
+V ──|         |─| |─| |─|     |─|     
 0   |─| |─| |─| |─| |─| |─| |─| |─| |─
-V     |─| |─|             |─|     |─| 

b) Bipolar NRZ

0 → 0 V. Each 1 → full-width pulse with polarity alternating + − + − +.

Bipolar NRZ

    1   0   0   1   1   1   0   1   0  
+V ────|           |───|       |───|   
 0     |───────|   |   |   |───|   |───
-V             |───|   |───|           

c) AMI

0 → 0 V. Each 1 → half-width pulse with polarity alternating + − + − +.

AMI (RZ)

    1   0   0   1   1   1   0   1   0  
+V ──|             |─|         |─|     
 0   |─────────| |─| |─| |─────| |─────
-V             |─|     |─|             

d) Manchester

Transition at every mid-bit: 1 → +V then −V, 0 → −V then +V.

Manchester

    1   0   0   1   1   1   0   1   0  
+V ──|   |─| |───| |─| |─|   |───|   |─
-V   |───| |─|   |─| |─| |───|   |───| 

✓ Answer checked by Claude Opus 5.5 (high effort)

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