1. Decimal Arithmetic (alternative to binary arithmetic)
numbers are stored as a series of base 10 digits  binary coded decimal (BCD) or  decimal arithmetic
two formats:
unpacked BCD → 8 bits = 1 decimal digit in low nibble e.g. 1,98510 = % = $
packed BCD → 8 bits = 2 decimal digits e.g. 1,98510 = % = $1985

2. Why Binary Coded Decimal (BCD)?
input/output from/to systems is typically ASCII
keypad systems (numbers only) are typically BCD
key press → ASCII or BCD digit
BCD arithmetic operations:
work on one byte at a time
assume packed BCD → 8 bits = 2 decimal digits
unpacked BCD only used in transition from ASCII to BCD → 8 bits = 1 decimal digit in low nibble

3. Why Binary Coded Decimal (BCD)?
if binary arithmetic:
input → ASCII
ASCII to BCD
BCD to binary
calc in binary
binary to BCD
BCD to ASCII
ASCII → output
if decimal arithmetic:
input → ASCII
ASCII to BCD
BCD to ASCII
ASCII → output

4. Decimal Arithmetic
operations: ABCD, SBCD, NBCD → byte only (2 BCD digits at a time)
start at the least significant byte and work to most significant byte
carry handled by using the X flag
ABCD (source)10 + (dest)10 + X → dest10
e.g. 1985
3459

5. Decimal Arithmetic … what really happens
Example 2
Example 1
Decimal Adjust Rules:
If sum > 9, then add 6
If carry from bit 3 to bit 4, then add 6 to the source of the carry.
Processors either:
provide BCD instructions (like 68000)
provide a decimal adjust instruction and a decimal carry in CCR (like Intel x86)
step 1 = binary add
step 2 = decimal adjust

6. Flags for BCD
clear X (extended carry) before first BCD operation so that carry is handled correctly
N and V are undefined for decimal arithmetic
sign is explicitly handled during the operation
C and X is set if decimal carry/borrow occurs
can be used to construct result if overflow
Z is cleared if the result is nonzero; otherwise unchanged
for addition, set Z to 1 before first BCD operation to obtain correct Z
no requirement to initialize Z if it is not important to the problem

7. Decimal Arithmetic
e.g. Add two numbers (bcdn1, bcdn2) and store result (bcdn2).
org $1000
start clr.w D2
move.b length,D2
subq.w #1,D2
lea bcdn1+4,A1
lea bcdn2+4,A0
move.w #$04,CCR
loop abcd.b -(A1),-(A0)
dbra D2,loop
stop #$2700
bcdn1 DC.L $
bcdn2 DC.L $
length DC.B 4
end start

8. BCD complements … signed numbers
1’s complement
flip all of the bits e.g –> 1100
or, alternatively, ≡ 1111 – 0011
2’s complement
1’s complement +1 e.g –> 1101
or, alternatively, ≡ ???? – 0011
9’s complement
10’s complement

10. Decimal Arithmetic … subtraction
e.g. 9999
- 4930
e.g. 1817
e.g
- ____ ____

11. you understand 9s and 10s complement you understand how NBCD works
Reading:
Mind-boggling math: BCD (binary coded decimal) [pdf]
[C. Maxfield -- EDN, 9/7/2005]
More mind-boggling math: Adding and subtracting unsigned BCD [pdf]
[C. Maxfield -- EDN, 9/21/2005]
Even more mind-boggling math: Working with signed BCD [pdf]
[C. Maxfield -- EDN, 10/5/2005]
NOTE: for the above references, the local PDF version is complete while the online EDN version is missing the diagrams.
M68000 Assembly Language [pdf, 92p; N. Znotinas]
review the decimal arithmetic (ABCD, SBCD, NBCD) instructions
Expectations:
you can write programs to do decimal arithmetic for numbers of unlimited width
you understand 9s and 10s complement
you understand how NBCD works
you know how to output negative BCD numbers as a negative decimal number (minus sign followed by the magnitude of the negative number)