Other Decimal Codes

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Binary codes for decimal digits require a minimum of four bits. Numerous different codes can be formulated by arranging four or more bits in 10 distinct possible combinations. A few possibilities are shown in Table 3-6.

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The BCD (binary-coded decimal) has been introduced before. It uses a straight assignment of the binary equivalent of the digit. The six unused bit combinations listed have no meaning when BCD is used, just as the letter H has no meaning when decimal digit symbols are written down. For example, saying that 1001 1110 is a decimal number in BCD is like saying that 9H is a decimal number in the conventional symbol designation. Both cases contain an invalid symbol and therefore designate a meaningless number.

self-complementing: One disadvantage of using BCD is the difficulty encountered when the 9's complement of the number is. to be computed. On the other hand, the 9's complement is easily obtained with the 2421 and the excess-3 codes listed self-complementing in Table 3-6. These two codes have a self-complementing property which means that the 9' s complement of a decimal number, when represented in one of these codes, is easily obtained by changing 1's to O's and O's to l's. This property is useful when arithmetic operations are done in signed-complement representation.

weighted code: The 2421 is an example of a weighted code. In a weighted code, the bits are multiplied by the weights indicated and the sum of the weighted bits gives the decimal digit. For example, the bit combination 1101, when weighted by the respective digits 2421, gives the decimal equivalent of 2 x 1 + 4 x 1 + 2 x 0 + 1 + 1 = 7. The BCD code can be assigned the weights 8421 and for this reason it is sometimes called the 8421 code.

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