Page 64 - Engineering Digital Design

2.4 UNSIGNED BINARY CODED DECIMAL, HEXADECIMAL, AND OCTAL 35

Table 2.2 BCD bit patterns and decimal equivalent

BCD BCD
Bit Pattern Decimal Bit Pattern Decimal
0000 0 1000 8
0001 1 1001 9
0010 2 1010 NA
0011 3 1011 NA
0100 4 1100 NA
0101 5 1101 NA
0110 6 1110 NA
0111 7 1111 NA
NA = not applicable (code words not valid)

polynomials of the form

1
2
3
#10 = b 3 x 2 + b 2 x 2 + b\ x 2 + b 0 x 2°
= & 3 x 8 + £ 2 x 4 + b, x 2 + £ 0 x 1
for any b^bibo code integer. Thus, decimal 6 is represented as (0 x 8) + (1 x 4) + (1 x
2) + (0 x 1) or 0110 in BCD code. As in binary, the bit positional weights of the BCD code
are derived from integer powers of 2". Table 2.2 shows the BCD bit patterns for decimal
integers 0 through 9.
Decimal numbers greater than nine or less than one can be represented by the BCD code
if each digit is given in that code and if the results are combined. For example, the number
63.98 is represented by (or converted to) the BCD code

6 3.9 8
63.98io = (01100011 . 1001 1000) BCD
= 1100011.1001IBCD

Here, the code weights are 80, 40, 20, 10; 8, 4, 2, 1; 0.8, 0.4, 0.2, 0.1; and 0.08, 0.04, 0.02,
0.01 for the tens, units, tenths, and hundredths digits, respectively, representing four decades.
Notice that the leading and trailing O's can be dropped. Pencil-and-paper conversion between
binary and BCD requires conversion to decimal as an intermediate step. For example, to
convert from BCD to binary requires that groups of four bits be selected in both directions
from the radix point to form the decimal number. If necessary, leading and trailing zeros
are added to the leftmost or rightmost ends to complete the groups of four bits as in the
example above. Negative BCD numbers are coded by using 10's complement notation as
discussed in a later section.
Another code that is used for number representation and manipulation is called Excess
3 BCD (or XS3 BCD or simply XS3). XS3 is an example of a biased-weighted code (a bias
of 3). This code is formed by adding 001 b (= 3io) to the BCD bit patterns in Table 2.2.