Data Acquisition

Table F.3 gives the conversion between decimal and binary numbers. Note that the binaryequivalent of decimal 15 is written in binary form as 1111 (using 4 bits). This 4 bit binarygrouping will have significance in hexadecimal arithmetic later. As expected binary 0 isequivalent to decimal 0.Table F.3Equivalent binary and decimal numbersThe procedure to convert from a binary number to a decimal number is straightforward.For example, to convert 1101.01 2 to decimal, use the weighting factors for each bit tomake the conversion.1101.01 2 = 1 × (2 3 ) + 1 × (2 2 ) + 1 × (2 1 ) + 1 × (2 0 ) + 1 × (2 -1 ) + 1 × (2 -2 )This is equivalent to:1101.01 2 = 1 × (8) + 1 × (4) + 1 × (2) + 1 × (1) + 1 × (½) + 1 × (¼)This then works out to:1101.01 2 = 8 + 4 + 0 + 1 + 0.251101.01 2 = 13.25The conversion process from a decimal number to a binary number is slightly morecomplex. The procedure here is to repeatedly divide the decimal number by two, until thequotient (the result of the division) is equal to zero. Each of the remainders forms theindividual bits of the binary number.