8b/10b Encoder & Decoder

What Is 8b/10b Encoding?

8b/10b is a line-coding system that converts each eight-bit input symbol into a ten-bit transmission code group. The additional encoded bits provide useful signal properties such as controlled disparity, sufficient transitions for clock recovery and special control symbols that cannot simply be treated as ordinary payload bytes.

The classic IBM implementation divides each byte into a five-bit portion and a three-bit portion. These are encoded through 5b/6b and 3b/4b coding tables, producing the final ten-bit code group.

A correct encoder cannot simply use a fixed lookup from each byte to one ten-bit value because the selected code group also depends on the current running disparity.

8b/10b D.x.y Symbol Notation

An ordinary data symbol is conventionally written as D.x.y. The five least significant input bits determine x, from 0 through 31, and the three most significant input bits determine y, from 0 through 7.

5b/6b and 3b/4b Encoding

The lower five data bits are transformed into a six-bit sub-block. The upper three bits are transformed into a four-bit sub-block.

Running disparity is evaluated during this process because the first sub-block can change the disparity state used to choose the second sub-block.

What Is Running Disparity?

Disparity is the difference between the number of transmitted ones and zeros. 8b/10b tracks a running state commonly represented as RD− or RD+.

When a sub-block has non-zero disparity, its selected version normally drives the running state toward the opposite sign. Balanced sub-blocks leave the state unchanged.

8b/10b Encoding Example: D31.1

D31.1 is a useful test of the encoder.

With initial RD+, the 5b/6b portion changes:

This illustrates why running disparity must be part of an 8b/10b encoder.

8b/10b K Control Symbols

8b/10b reserves several legal control characters known as K symbols. They are not ordinary data bytes even though each can be associated with an eight-bit value.

This calculator accepts the standard control set:

K28.5 8b/10b Encoding

K28.5 is one of the best-known 8b/10b control characters and is commonly used as a comma-related synchronization symbol by protocols built on 8b/10b.

The decoder recognizes both forms and checks whether the selected one is legal for the running disparity entering that code group.

What Is an 8b/10b Disparity Error?

A received ten-bit pattern may be a legitimate 8b/10b code group but still be wrong for the receiver’s current running disparity.

That situation is different from receiving a pattern that is not a legal 8b/10b symbol at all.

Why the Decoder Tracks Running Disparity

Suppose a code group is valid only when entering the symbol with RD+. If the receiver is currently in RD− and receives that RD+ form, simply looking up the ten bits would identify the underlying symbol but miss an important line-code violation.

This decoder therefore builds both the legal code map and the expected-RD map. It can report a recognizable symbol as a disparity error rather than treating every recognizable ten-bit pattern as valid.

8b/10b Expansion Ratio

Eight application bits become ten transmitted bits:

The physical encoded bit count is therefore 25% larger than the original eight-bit symbol count before considering any higher-level protocol framing.

Why 8b/10b Uses Alternative Encodings

Many symbols have different legal code groups for negative and positive running disparity. These choices allow the transmitter to keep the long-term difference between ones and zeros bounded instead of allowing a large DC imbalance to accumulate.

Some balanced sub-blocks use the same pattern for both running states, while others have special alternate representations selected for run-length and coding constraints.

Special Alternate .7 Encoding

The three-bit value 7 has primary and alternate 3b/4b representations in specific circumstances. Correct handling of those alternatives helps prevent undesirable long runs and is one reason a simple independent lookup of the 5b and 3b fields is not sufficient for a complete encoder.

The JavaScript implementation on this page applies the standard alternate D.x.A7 conditions and uses the appropriate alternate code for legal K.x.7 control symbols.

Bit Order Used by This Calculator

The calculator displays the conventional 8b/10b code-group notation:

The six-bit 5b/6b group is shown first, followed by the four-bit 3b/4b group. This is the representation commonly used in published 8b/10b tables.

Encoding Multiple 8b/10b Symbols

When several bytes are encoded, running disparity is not reset for each byte. The RD output from one symbol becomes the RD input to the next symbol.

This is why the tool supports complete sequences rather than calculating every byte independently.

Hexadecimal to 8b/10b Encoding

Hex mode interprets every two hexadecimal digits as one ordinary eight-bit data symbol. For each byte, the tool derives x from the low five bits and y from the upper three bits.

Note that ordinary hexadecimal input always means a D data character. If you specifically require the control character having the same underlying byte value, enter the appropriate K.x.y notation in Symbol mode.

D Symbol vs K Symbol

A byte value alone is not sufficient to say that a character is a K control character. The transmitter must intentionally request a legal K code.

Their 8b/10b code groups are not generally interchangeable, so this calculator keeps the two cases explicit.

Invalid K Codes

Only the defined K symbol set can be encoded. For example, a user cannot arbitrarily request K1.2 simply because x and y fall within the numerical D.x.y ranges.

When an illegal K symbol is entered, the encoder rejects it instead of silently treating it as ordinary data.

Common 8b/10b Encoding Mistakes

8b/10b Encoder & Decoder FAQs