The document discusses binary addition and provides examples of applying the rules of binary addition. It begins by stating the goal of correctly applying the rules of binary addition. It then lists the 4 rules of binary addition and provides examples of applying each rule. It concludes by providing multiple multi-bit binary addition examples that demonstrate applying the rules to obtain the sum.

1. 1.12
10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Binary Addition
MATH1003

2. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Goal
To correctly apply the rules of binary addition.
MATH1003

3. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Rules of Binary Addition
MATH1003

4. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Rules of Binary Addition
Rule 1
0
+0
0
MATH1003

5. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Rules of Binary Addition
Rule 1 Rule 2
0 0 1
+0 +1 +0
0 1 1
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6. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Rules of Binary Addition
Rule 1 Rule 2 Rule 3
0 0 1 1
+0 +1 +0 +1
0 1 1 10
MATH1003

7. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Rules of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
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8. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
111012
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9. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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10. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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11. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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12. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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13. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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14. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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15. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
101002
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 10012
111012
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16. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
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17. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
0
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18. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
0
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19. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
00
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20. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
00
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21. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
000
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22. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
000
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23. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
0000
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24. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
10000
MATH1003

25. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
10112
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1012
100002
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26. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
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27. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
0
MATH1003

28. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
0
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29. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
00
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30. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
00
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31. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
000
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32. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
000
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33. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
1000
MATH1003

34. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
1000
MATH1003

35. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
11000
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36. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
011000
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37. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
1011000
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38. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1011012
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 1010112
10110002
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39. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
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40. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
1
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41. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
01
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42. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
.01
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43. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
.01
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44. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
0.01
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45. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
0.01
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46. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
10.01
MATH1003

47. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
10.01
MATH1003

48. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
010.01
MATH1003

49. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
010.01
MATH1003

50. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
0010.01
MATH1003

51. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
10010.01
MATH1003

52. 10110100101011010100101010111010101111011011101111011101110111101110111011110111111010110100101011110110110101111011010100111111011010100110101001
Examples of Binary Addition
Rule 1 Rule 2 Rule 3 Rule 4
1 1 1 1 1
1110.102
0 0 1 1 1
+0 +1 +0 +1 +1
0 1 1 10 11
+ 011.112
10010.012
MATH1003