Binary-Coded Decimal Code

Binary-Coded Decimal Code

Although the binary number system is the most natural system for a computer because it is readily represented in today’s electronic technology, most people are more accustomed to the decimal system. One way to resolve this difference is to convert decimal numbers to binary, perform all arithmetic calculations in binary, and then convert the binary results back to decimal. This method requires that we store decimal numbers in the computer so that they can be converted to binary. Since the computer can accept only binary values, we must represent the decimal digits by means of a code that contains 1’s and 0’s. It is also possible to perform the arithmetic operations directly on decimal numbers when they are stored in the computer in coded form.

            A binary code will have some unassigned bit combinations if the number of elements in the set is not a multiple power of 2. The 10 decimal digits form such a set. A binary code that distinguishes among 10 elements must contain at least four bits, but 6 out of the 16 possible combinations remain unassigned. Different binary codes can be obtained by arranging four bits into 10 distinct combinations. The code most commonly used for the decimal digits is the straight binary assignment listed in Table 1.4 . This scheme is called binary‐coded decimal and is commonly referred to as BCD. Other decimal codes are possible and a few of them are presented later in this section.

Table 1.4 gives the four‐bit code for one decimal digit. A number with k decimal

digits will require 4k bits in BCD. Decimal 396 is represented in BCD with 12 bits as 0011 1001 0110, with each group of 4 bits representing one decimal digit. A decimal number in BCD is the same as its equivalent binary number only when the number is between 0 and 9. A BCD number greater than 10 looks different from its equivalent binary number, even though both contain 1’s and 0’s. Moreover, the binary combinations 1010 through 1111 are not used and have no meaning in BCD. Consider decimal 185 and its corresponding value in BCD and binary:

(185)10 = (0001 1000 0101)BCD = (10111001)2

Digital Systems and Binary Numbers :

The BCD value has 12 bits to encode the characters of the decimal value, but the equivalent binary number needs only 8 bits. It is obvious that the representation of a BCD number needs more bits than its equivalent binary value. However, there is an advantage in the use of decimal numbers, because computer input and output data are generated by people who use the decimal system.

            It is important to realize that BCD numbers are decimal numbers and not binary numbers, although they use bits in their representation. The only difference between a decimal number and BCD is that decimals are written with the symbols 0, 1, 2, c, 9 and BCD numbers use the binary code 0000, 0001, 0010, c, 1001. The decimal value is exactly the same. Decimal 10 is represented in BCD with eight bits as 0001 0000 and decimal 15 as 0001 0101. The corresponding binary values are 1010 and 1111 and have only four bits.