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Binary, Decimal, Hexadecimal

Topics:

  • Introduction
  • Binary
  • Decimal
  • Hexadecimal
  • Convert binary to decimal
  • Convert decimal to binary
  • Convert binary to hexadecimal
  • Convert hexadecimal to binary

Introduction:
All computers in the car operate with digital electronics: the numbers 1 and 0. If computer A wants to send certain information to computer B via the CAN bus, a message consisting entirely of 1s and 0s is created (binary), then converted to a decimal or hexadecimal message, which is recognized and processed by computer B. The processor of the computer always works internally with ones and zeros. Therefore, the decimal and hexadecimal codes from the sensors and other computers must always be converted. 1 means ‘on’ and 0 means ‘off’.

The binary system is used internally by control units. Binary codes can also be used for small data transmissions, e.g., switch on (1) or off (0). For larger data transmissions, such as from a temperature sensor, many ones and zeros must be sent. A hexadecimal system can transmit the temperature much more accurately via the data bus, because many more different temperatures can be communicated between 00 and FF than the combinations of ones and zeros in the binary system. The codes can also be manually converted. How this works is explained further on this page.

Binary:
Binary system: 01
Possibility: 0 or 1

Practical example: A window switch sends a decimal code of 252 via the data bus to the control unit. The code is converted by the control unit into a binary code of 11111100. The control unit recognizes that this is the code to open the right front window. The control unit supplies power to the window motor until the switch sends the code 00000000, or until the window reaches the end position.

Left front window open: 11111110 Close: 01111111
Right front window open: 11111100 Close: 00111111
Left rear window open: 11111000 Close: 00011111
Right rear window open: 11110000 Close: 00001111
Switches idle position: 00000000 Fault: 11111111

Decimal:
Decimal system: 0123456789
Possibility: Between 0 and 255

A decimal number can be seen as a compact binary number. A binary value of: 01100100 is decimal: 100.

Hexadecimal:
Hexadecimal system: 0123456789ABCDEF
Possibility: Between 00 and FF

The hexadecimal system is more extensive than the decimal system. The hex goes from 0 to 15, while the deci goes from 0 to 9.
Numbers higher than 9 are indicated with letters:
10 = A
11 = B
12 = C
13 = D
14 = E
15 = F
This provides more possibilities than the decimal system and will be ideal for control units with large data transmissions.

Convert binary to decimal:

Convert decimal to binary:

Convert binary to hexadecimal:

Convert hexadecimal to binary:

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