The decimal system has a base of 10. The base of a number system determines the total number of different symbols or digits used by that system. The value of a decimal number depends on the digits that make up the number and the place value of each digit. In the decimal system the first position, starting from the furthest right position, is 0; the second is 1; and so on up to the last position. The weighted value of each position can be expressed as the base raised to the power of the position.
The binary numbering system is the basis of all digital system. Two states exist in digital equipment, an ON state which is representative of one (1), and an OFF condition which is representative of zero (0). The decimal equivalent of a binary number is calculated in a manner similar to that used for a decimal number. The weighted value is 2 raised to the power of the position.
Each digit of a binary number is known as a bit. Bit can also be grouped within a word into bytes. The least significant bit (LSB) is the digit that represents the smallest value, and the most significant bit (MSB) is the digit that represents the largest value.
The octal numbering system, a base 8 system, is often used in microprocessor, computer, and programmable controller systems because 8 data bits make up a byte of information which can be addressed by the PLC user or programmer.
The hexadecimal (hex) number system provides even shorter notation than octal. Hexadecimal uses a base of 16. It employs 16 digits: numbers 0 through 9, and letters A through F, with A through F being substituted for numbers 10 through 15, respectively.
The binary coded decimal (BCD) system provides a convenient means to handle large numbers that need to be input to or output from PLC. The BCD system represents decimal numbers as patterns of 1s and 0s. This system provides a means of converting a code readily handled by humans (decimal) to a code readily handled by the equipment (binary). The BCD code employs 4 binary bits, with the weights of 1, 2, 4, and 8, to represent each numeral in the decimal system.
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