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2.9 BINARY ARITHMETIC 63

EXAMPLE 2.32
056io -> 0000 0101 OllOfiCD Augend A BCD
+06910 -> +0000 0110 lOOlgcp Addend B BCD
125,0 0000 1011 1111 Sum
0110 0110 Correction
1 1111 110 Carries
0001 0010 0101 BCD Result = 125 w
The following algorithm generalizes the process just given for operands having both
integers and fractions.

Algorithm 2.14: A BCD + BBCD
(1) Set BCD operands in descending decade order, ABCD = • • • AiooAioAjA.iA.oi • • •
and BBCD = • • • B mBi QB { B A B M • • • such that the MSDs for A and B are 0000 (null).
(2) Set i = LSD for matching operand decades.
(3) If A f + Bi > 1001 by Algorithm 2,8, add 0110 to that result and carry 0001 over
to the next MSD. If A ( + B { < 1001, add 0000 to the result and carry 0000 to the next
MSD.
l
2
3
(4) Repeat steps (2) and (3) for matching decades in the order of W i, I0 i, 10 z,...,
MSD.
BCD Subtraction Negative BCD numbers are most conveniently represented in 10's
complement (IOC). This permits negative BCD numbers to be added according to Algo-
rithm 2.14. The result, if negative, will be represented in IOC form requiring negation to
obtain the true value.
EXAMPLE 2.33
08.25io -» 08.25,0 -> 0000 1000.0010 0101 BCD
-13.52,0 -> +86.48| OC -> +1000 0110.0100 1000 BCD) IOC
-05.27,0 94.73 ,oc 1000 1110.0110 1101 Sum
+ 0110 0110 Correction
1 11 1_J Carries
1001 0100.0111 0011 BCD) 10C Result
The true (absolute) value of the result is found by negation to be

94.73,oc)ioc = 05.27,0 or 0000 0101.0010 Oil 1 BCD-

Note that to convert directly from the BCD form, flCD), 0c = N 2c + 1010 = N 2 +
ILSB + 1010 for the LSD but thereafter is fiCD), oc = N 2 + 1010 = N 9C, discarding any
carry overflow in either case.
The following algorithm generalizes the process of BCD subtraction.

Algorithm 2.15: A BCD + B BCD) m or A BCD) 10C + B BCD) m
(1) Convert any negative decimal number to its 10's complement (IOC) by Algorithm 2.5
with r = 10.