# What is ab c d 4

## BCD code - Binary Coded Decimals

In addition to the number systems, there are also codes to represent and process numbers digitally. The BCD code stands for Binary Coded Decimals, which means binary coded decimal digits. What is meant are dual-coded numbers. In the BCD code, each decimal digit is represented by 4 bits of the corresponding dual number.
Another name is 8-4-2-1-BCD-Code, because it is the decimal value of the dual digits.

Decimal23222120
10001
20010
30011
40100
50101
60110
70111
81000
91001
1011
1100
1101
1110
1111

Each decimal digit of the decimal number is expressed by its own 4-bit binary number or binary code. The 4 bits are called a tetrad (Greek: group of four).
Only 10 tetrads are required for the 10 decimal digit. The 6 other tetrads are called pseudotetrads and no longer belong to them. They are omitted or have no function. They do not appear or must not appear in the BCD code.

DecimalBCD
0 00000 0000
0 10000 0001
0 20000 0010
0 30000 0011
0 40000 0100
0 50000 0101
0 60000 0110
0 70000 0111
0 80000 1000
0 90000 1001
1 00001 0000
1 10001 0001
1 20001 0010
1 30001 0011
1 40001 0100
1 50001 0101
1 60001 0110
1 70001 0111
1 80001 1000
1 90001 1001
2 00010 0000
2 10010 0001
2 20010 0010
2 30010 0011

### Identification of the BCD code

Bit sequence: 1001 = 1001BCD = 910

Bit sequence: 1000111 = 0100 0111BCD = 4710

### Disadvantage of the BCD code

For a three-digit decimal number from 0 to 999 you would need 10 bits as the binary number (11111001112). 12 bits are required as a binary coded decimal number (0011 1110 0111BCD).
Therefore, in practice, instead of BCD, other codes are used that are not so wasteful.

### Applications

BCD arithmetic is rarely used. The memory is being used too wastefully. And compared to 32-bit floating point numbers, BCD numbers only provide a slightly higher level of precision. However, there is still a need in finance and science for very high accuracy that goes beyond floating point representation. There is, for example, Densely Packed Decimal Encoding, which is supported by the hardware on some computers or is available via software libraries. For mainframe computers as well as technical-scientific pocket calculators.

BCD coding is used in digital technology and digital displays. For example as a 7-segment display.
Digital clocks run inside with BCD code. The time in the DCF77 signal is also encoded as a BCD code.

### 7-segment display

A BCD decoder and a 7-segment display are used to display the 4-bit binary number as a decimal number. The 7-segment display has 7 light strips that are arranged like an 8. The BCD decoder decodes the BCD code (4-bit) to the 7 segments.

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