- 1). Write the BCD code for a number you need to convert to a base. The BCD code is a series of 4-bit binary numbers that correspond to each digit in the base number system. For example, using the base 10 or decimal system number 138, the BCD code has 12 bits. Each 4 bits represents a single digit in the decimal number. The first digit is 1 so the BCD code is 0001. The next two digits are composed in the same manner, namely 3 is 0011 and 8 is 1000. The BCD code representation of decimal 138 is 000100111000 or simplified as 100111000.
- 2). Select the number base into which you want the BCD coded number converted. The most common bases used in computer programming are binary (base 2), octal (base 8) and hexadecimal (base 16).
- 3). Decode the BCD coded number into decimal format. There is no direct way to convert BCD code to a different base. To write the number in a base of your choosing you must convert from decimal to that base. For example, decode the following BCD coded decimal number (Base 10), 1001011100101001. Convert the BCD code into the decimal number by grouping the bits into sets of 4 bits and then convert each group of four bits into the decimal digit. The four groups are 1001, 0111, 0010 and 1001. These convert to 9729.
- 4). Divide the decimal number by the value of the base you are converting into. The remainder of the division fills in the least significant position of the result. Divide the integer portion of the result by the value of the base again. The integer portion carries forward and the remainder of the division fills into the next least significant position in the result. This continues until the integer portion is too small to divide by the value of the base. For example, convert 312 decimal into base 4. The following series of calculations will yield the answer in base 4. 312 / 4 = 78 remainder 0. Least significant digit of answer 0. 78 / 4 = 19 remainder 0.5. The next digit in the answer is 4 x 0.5 = 2. 19 / 4 = 4 remainder 0.75. The next digit is 0.75 x 4 = 3. 4 / 4 = 1 remainder 0. The next digit is 0. The next digit in the answer is 1 / 4 = remainder 0.25. The last digit is 0.25 x 4 = 1. Put these together to get the answer, 10320 base 4.
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