In differential Manchester, how is data carried?

0 = transition at start of bit, 1 = no transition at start; there is always a mid-bit transition

1 = transition at start of bit, 0 = no transition

By the polarity of the mid-bit transition only

In HDB3, a run of four zeros is replaced by 000V or B00V. When is B00V used?

When the number of pulses since the last substitution is even

When the number of pulses since the last substitution is odd

How do the bandwidths compare?

HDB3 and B8ZS need about Rb, half of polar RZ and differential Manchester (2Rb)

HDB3 and B8ZS need about 2Rb, polar RZ needs Rb

2081 Chaitra · 10 marks

Line coding 100000000001101 with HDB3 and B8ZS

Short answer

Polar RZ: half-width ±V pulses. Differential Manchester: mid‑bit transition always; start transition for 0, none for 1. HDB3: AMI with 000V or B00V replacing 4 zeros. B8ZS: AMI with 000VB0VB replacing 8 zeros. Bandwidths: Polar RZ and Diff Manchester ≈ 2Rb; HDB3 and B8ZS ≈ Rb, all with no DC.

Consider that the bit sequence 100000000001101 is to be transmitted. Draw the resulting waveform if the sequence is transmitted using Polar RZ, Differential Manchester, HDB3 and B8ZS, and compare their bandwidths.

Bit sequence: 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1 (15 bits: a 1, ten 0s, then 1101). Each waveform is drawn in two parts: bits 1–8, then bits 9–15.

Polar RZ

1 is sent as a +V pulse for half the bit, and 0 as a −V pulse for half the bit. The line returns to zero in the second half of every bit.

Polar RZ

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

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

Differential Manchester

There is always a transition at the middle of each bit (used for the clock). Data is carried by the start of the bit: 0 = transition at the start, 1 = no transition at the start. The line is assumed to be at −V before the first bit.

Differential Manchester

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

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

HDB3 (High Density Bipolar 3)

HDB3 is AMI, except that every run of four 0s is replaced:

000V if the number of pulses since the last substitution is odd,
B00V if it is even.

V (violation) has the same polarity as the pulse before it. B follows the normal AMI rule. This makes successive V pulses alternate, so no DC builds up.

Bit 1 → +.
Zeros 2–5: 1 pulse since start (odd) → 000V = 0 0 0 +.
Zeros 6–9: 0 pulses since the last V (even) → B00V = − 0 0 −.
Zeros 10–11 → 0 0.
1101 → + − 0 +.

HDB3 pulses: + 0 0 0 + − 0 0 − 0 0 + − 0 +

HDB3 (half-width pulses)

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

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

B8ZS (Bipolar with 8-Zero Substitution)

B8ZS is AMI, except that every run of eight 0s is replaced by 000VB0VB. Taking the previous pulse as +, the substitute is 0 0 0 + − 0 − +.

Bit 1 → +.
Zeros 2–9 → 0 0 0 + − 0 − +.
Zeros 10–11 → 0 0.
1101: the last pulse was +, so this gives − + 0 −.

B8ZS pulses: + 0 0 0 + − 0 − + 0 0 − + 0 −

B8ZS (half-width pulses)

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

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

Bandwidth comparison

Code	Main-lobe (first-null) bandwidth	DC component	Remarks
Polar RZ	$2R_b$	None (equiprobable bits)	Pulses half-width, so double bandwidth
Differential Manchester	$2R_b$	None	Self-clocking, polarity-insensitive
HDB3	$R_b$ (most power near $R_b/2$ )	None	Bipolar; keeps timing on long 0 runs (E1)
B8ZS	$R_b$ (most power near $R_b/2$ )	None	Bipolar; keeps timing on long 0 runs (T1)

HDB3 and B8ZS need about half the bandwidth of polar RZ and differential Manchester, and they still keep timing information when long strings of 0s occur.

✓ Answer checked by Claude Opus 5.5 (high effort)

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