Data Acquisition

• Decimal with ten symbols (0, l, 2...9) and hence a base of 10When numbers with different bases are being used in the same descriptive text theysometimes have the subscript referring to the base being used, as in 3421.19 10 for adecimal or base 10 number.Numerical symbols have to be combined in a certain way to represent othercombinations of numbers. The decimal numbering system has the structure laid out inTable F.1 for weighting each digit in the number 3421.19 10 in a combination of numberswritten together.Exponential notation is used here, where for example: 10 2 means 100 and to 10 –3 means0.001. Table F.1Decimal weighting systemThe most significant digit (or MSD) in this number is 3. This refers to the left mostnon-zero digit that has the greatest weight (10 3 or 1000) assigned to it.The least significant digit (or LSD) in this number is 9. This refers to the right mostnon-zero digit that has the least weight (10 -2 or 0.01) assigned to it.This represents the number calculated below:0 × 10 4 + 3 × 10 3 + 4 × 10 2 + 2 × 10 1 + 1 × 10 0 + 1 × 10 -1 + 9 × 10 -2 + 0 × 10 -3 +...F.3 Binary numbersBinary numbers are commonly used with computers and data communications becausethey represent two states – either ON or OFF. For example, the RS-232-C standard hastwo voltages assigned for indicating ON (–5 volts, say) or OFF (+5 Volts, say). Any othervoltages outside a narrow band around these voltages are undefined.The word ‘bit’, referred to often in the literature, is a contraction of the words ‘binarydigit’.The same principles for representing a binary number apply as in the previous section.For example, the number 1011.1 2 means the following using Table F.2: Table F.2Binary weighting systemThis translates into the following number:……..0 × 2 4 + 1 × 2 3 + 0 × 2 2 + 1 × 2 1 + 1 × 2 0 + 1 × 2 -1 + 0 × 2 -2 + ……..The most significant bit (MSB) in the above number is the left most bit and is 1 withweighting of 2 3 . The right most bit is the least significant bit (LSB) and is valued at 1with a weighting of 2 -1 .