In the tables in Appendix A, underlining denotes signed overflow.
The table for subtraction (Table A-2) assumes that the carry bit for a - b is set as it would be for a + b?/span> + 1, so that carry is equivalent to "not borrow."
For multiplication (Tables A-3 and A-4), overflow means that the result cannot be expressed as a 4-bit quantity. For signed multiplication (Table A-3), this is equivalent to the first five bits of the 8-bit result not being all 1's or all 0's.
Table A-4.. Unsigned Multiplication |
||||||||||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
2 |
0 |
2 |
4 |
6 |
8 |
A |
C |
E |
10 |
12 |
14 |
16 |
18 |
1A |
1C |
1E |
3 |
0 |
3 |
6 |
9 |
C |
F |
12 |
15 |
18 |
1B |
1E |
21 |
24 |
27 |
2A |
2D |
4 |
0 |
4 |
8 |
C |
10 |
14 |
18 |
1C |
20 |
24 |
28 |
2C |
30 |
34 |
38 |
3C |
5 |
0 |
5 |
A |
F |
14 |
19 |
1E |
23 |
28 |
2D |
32 |
37 |
3C |
41 |
46 |
4B |
6 |
0 |
6 |
C |
12 |
18 |
1E |
24 |
2A |
30 |
36 |
3C |
42 |
48 |
4E |
54 |
5A |
7 |
0 |
7 |
E |
15 |
1C |
23 |
2A |
31 |
38 |
3F |
46 |
4D |
54 |
5B |
62 |
69 |
8 |
0 |
8 |
10 |
18 |
20 |
28 |
30 |
38 |
40 |
48 |
50 |
58 |
60 |
68 |
70 |
78 |
9 |
0 |
9 |
12 |
1B |
24 |
2D |
36 |
3F |
48 |
51 |
5A |
63 |
6C |
75 |
7E |
87 |
A |
0 |
A |
14 |
1E |
28 |
32 |
3C |
46 |
50 |
5A |
64 |
6E |
78 |
82 |
8C |
96 |
B |
0 |
B |
16 |
21 |
2C |
37 |
42 |
4D |
58 |
63 |
6E |
79 |
84 |
8F |
9A |
A5 |
C |
0 |
C |
18 |
24 |
30 |
3C |
48 |
54 |
60 |
6C |
78 |
84 |
90 |
9C |
A8 |
B4 |
D |
0 |
D |
1A |
27 |
34 |
41 |
4E |
5B |
68 |
75 |
82 |
8F |
9C |
A9 |
B6 |
C3 |
E |
0 |
E |
1C |
2A |
38 |
46 |
54 |
62 |
70 |
7E |
8C |
9A |
A8 |
B6 |
C4 |
D2 |
F |
0 |
F |
1E |
2D |
3C |
4B |
5A |
69 |
78 |
87 |
96 |
A5 |
B4 |
C3 |
D2 |
E1 |
Tables A-5 and A-6 are for conventional truncating division. Table A-5 shows a result of 8 with overflow for the case of the maximum negative number divided by -1, but on most machines the result in this case is undefined, or the operation is suppressed.
Table A-6.. Unsigned Short Division (row ?column) |
||||||||||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
0 |
- |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
- |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
2 |
- |
2 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
3 |
- |
3 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
4 |
- |
4 |
2 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
5 |
- |
5 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
6 |
- |
6 |
3 |
2 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
7 |
- |
7 |
3 |
2 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
8 |
- |
8 |
4 |
2 |
2 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
9 |
- |
9 |
4 |
3 |
2 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
A |
- |
A |
5 |
3 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
B |
- |
B |
5 |
3 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
C |
- |
C |
6 |
4 |
3 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
0 |
D |
- |
D |
6 |
4 |
3 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
0 |
E |
- |
E |
7 |
4 |
3 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
0 |
F |
- |
F |
7 |
5 |
3 |
3 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
Tables A-7 and A-8 give the remainder associated with conventional truncating division. Table A-7 shows a result of 0 for the case of the maximum negative number divided by -1, but on most machines the result for this case is undefined, or the operation is suppressed.
Table A-8.. Remainder for Unsigned Short Division (row ?column) |
||||||||||||||||
|
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
A |
B |
C |
D |
E |
F |
0 |
- |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
- |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
- |
0 |
0 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
2 |
3 |
- |
0 |
1 |
0 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
4 |
- |
0 |
0 |
1 |
0 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
4 |
5 |
- |
0 |
1 |
2 |
1 |
0 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
6 |
- |
0 |
0 |
0 |
2 |
1 |
0 |
6 |
6 |
6 |
6 |
6 |
6 |
6 |
6 |
6 |
7 |
- |
0 |
1 |
1 |
3 |
2 |
1 |
0 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
7 |
8 |
- |
0 |
0 |
2 |
0 |
3 |
2 |
1 |
0 |
8 |
8 |
8 |
8 |
8 |
8 |
8 |
9 |
- |
0 |
1 |
0 |
1 |
4 |
3 |
2 |
1 |
0 |
9 |
9 |
9 |
9 |
9 |
9 |
A |
- |
0 |
0 |
1 |
2 |
0 |
4 |
3 |
2 |
1 |
0 |
A |
A |
A |
A |
A |
B |
- |
0 |
1 |
2 |
3 |
1 |
5 |
4 |
3 |
2 |
1 |
0 |
B |
B |
B |
B |
C |
- |
0 |
0 |
0 |
0 |
2 |
0 |
5 |
4 |
3 |
2 |
1 |
0 |
C |
C |
C |
D |
- |
0 |
1 |
1 |
1 |
3 |
1 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
D |
D |
E |
- |
0 |
0 |
2 |
2 |
4 |
2 |
0 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |
E |
F |
- |
0 |
1 |
0 |
3 |
0 |
3 |
1 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |