BCD counting code

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properties
Number of digits: 10
Evaluable: Yes
Weight: 1… 10
Minimum distance: 1
Maximum distance: 9
Hamming distance 1
Steady: Yes
Redundancy : 6.7
Code table
Digit coded
0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 1
2 0 0 0 0 0 0 0 0 1 1
3 0 0 0 0 0 0 0 1 1 1
4th 0 0 0 0 0 0 1 1 1 1
5 0 0 0 0 0 1 1 1 1 1
6th 0 0 0 0 1 1 1 1 1 1
7th 0 0 0 1 1 1 1 1 1 1
8th 0 0 1 1 1 1 1 1 1 1
9 0 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1 1

The BCD counting code ( unary coding ) encodes a decimal digit in binary representation; In contrast to the BCD code , each digit here has the value one.

Compare BCD to BCD counting code

As an example, let's compare the coding of the decimal digit 5:

BCD code:

BCD counting code:

Areas of application

The BCD counting code is mainly used to control machines. Similar to the Gray code , because of its one-step nature ( Hamming distance = 1), no jump errors occur. Jump error means that when switching from one state to the next, more than one bit has to be changed, but in most cases this can only be done sequentially and therefore an irregular intermediate state is temporarily reached, which must be avoided. For this reason, the very high redundancy of the code (6.7) is accepted.

Fixed-length unar coding is used in neural networks to ensure that learning a particular point enables learning of all neighboring ( Hamming distance ) points.

See also

Individual evidence

  1. ↑ a b Normal Unary Codes. (PDF) Retrieved September 12, 2018 (English).
  2. ↑ Subhash Kak: Spread Unary coding. (PDF; 594 kB) Oklahoma State University, accessed on September 12, 2018 (English).
  3. ↑ Error Correction Capacity of Unary coding. (PDF) Retrieved September 12, 2018 (English).
  4. ↑ Unary Coding for Neural Network Learning. (PDF) Retrieved September 12, 2018 (English).