# 4B3T

**4B3T**, which stands for 4 (four) Binary 3 (three) Ternary, is a line encoding scheme used for ISDN PRI interface. 4B3T represents four binary bits using three pulses.

## Description

It uses three states:

- + (positive pulse),
- 0 (no pulse), and
- − (negative pulse).

This means we have 2^{4} = 16 input combinations to represent, using 3^{3} = 27 output combinations. 000 is not used to avoid long periods without a transition. 4B3T uses a paired disparity code to achieve an overall zero DC bias: six triplets are used which have no DC component (0+−, 0−+, +0−, −0+, +−0, −+0), and the remaining 20 are grouped into 10 pairs with differing disparity (e.g. ++− and −−+). When transmitting, the DC bias is tracked and a combination chosen that has a DC component of the opposite sign to the running total.

This mapping from 4 bits to three ternary states is given in a table known as Modified Monitoring State 43 (MMS43). A competing encoding technique, used for the ISDN basic rate interface where 4B3T is not used, is 2B1Q.

The sync sequence used is the 11-symbol Barker code, +++−−−+−−+− or its reverse, −+−−+−−−+++.

## Encoding table

Each 4-bit input group is encoded as a 3-symbol group (transmitted left to right) from the following table. Encoding requires keeping track of the accumulated DC offset, the number of + pulses minus the number of − pulses in all preceding groups. The starting value is arbitrary; here we use the values 1 through 4, although −1.5, −0.5, +0.5 and +1.5 is another possibility.

Input | Accumulated DC offset | ||||
---|---|---|---|---|---|

Hex | Binary | 1 | 2 | 3 | 4 |

0 | 0000 | + 0 + (+2) | 0−0 (−1) | ||

1 | 0001 | 0 − + (+0) | |||

2 | 0010 | + − 0 (+0) | |||

3 | 0011 | 0 0 + (+1) | − − 0 (−2) | ||

4 | 0100 | − + 0 (+0) | |||

5 | 0101 | 0 + + (+2) | − 0 0 (−1) | ||

6 | 0110 | − + + (+1) | − − + (−1) | ||

7 | 0111 | − 0 + (+0) | |||

8 | 1000 | + 0 0 (+1) | 0 − − (−2) | ||

9 | 1001 | + − + (+1) | − − − (−3) | ||

A | 1010 | + + − (+1) | + − − (−1) | ||

B | 1011 | + 0 − (+0) | |||

C | 1100 | + + + (+3) | − + − (−1) | ||

D | 1101 | 0 + 0 (+1) | − 0 − (−2) | ||

E | 1110 | 0 + − (+0) | |||

F | 1111 | + + 0 (+2) | 0 0 − (−1) |

This code forces a transition after at most five consecutive identical non-zero symbols, or four consecutive zero symbols.

## Decoding table

Decoding is simpler, as the decoder does not need to keep track of the encoder state, although doing so allows greater error detection. The 000 triplet is not a legal encoded sequence, but is typically decoded as binary 0000.

Ternary | Binary | Hex | Ternary | Binary | Hex | Ternary | Binary | Hex | ||
---|---|---|---|---|---|---|---|---|---|---|

0 0 0 | N/A | N/A | − 0 0 | 0101 | 5 | + − − | 1010 | A | ||

+ 0 + | 0000 | 0 | − + + | 0110 | 6 | + 0 − | 1011 | B | ||

0 − 0 | 0000 | 0 | − − + | 0110 | 6 | + + + | 1100 | C | ||

0 − + | 0001 | 1 | − 0 + | 0111 | 7 | − + − | 1100 | C | ||

+ − 0 | 0010 | 2 | + 0 0 | 1000 | 8 | 0 + 0 | 1101 | D | ||

0 0 + | 0011 | 3 | 0 − − | 1000 | 8 | − 0 − | 1101 | D | ||

− − 0 | 0011 | 3 | + − + | 1001 | 9 | 0 + − | 1110 | E | ||

− + 0 | 0100 | 4 | − − − | 1001 | 9 | + + 0 | 1111 | F | ||

0 + + | 0101 | 5 | + + − | 1010 | A | 0 0 − | 1111 | F |

## See also

Other line codes that have 3 states:

## References

- "Wired Communications T-SMINTO 4B3T Second Gen. Modular ISDN NT (Ordinary)" (PDF) (Data sheet). Version 1.1. Infineon. November 2001. PEF 80902.