1. Decimal Addition 111 3758 + 4657 8415 What is going on? 1 1 1 (carry) 3 7 5 8 + 4 6 5 7 14 11 15 - 10 10 10 (subtract the base) 8 4 1 5

2. Binary Addition Rules. –0 + 0 = 0 –0 + 1 = 1 –1 + 0 = 1 –1 + 1 = 2 = 10 2 = 0 with 1 to carry –1 + 1 + 1 = 3 = 11 2 = 1 with 1 to carry

3. Binary Addition 1 1 1 1 1 1 0 1 1 1 + 0 1 1 1 0 0 2 3 2 2 - 2 2 2 2 1 0 1 0 0 1 1 Verification 55 10 + 28 10 83 10 64 32 16 8 4 2 1 1 0 1 0 0 1 1 = 64 + 16 + 2 +1 = 83 10

4. Binary Addition ex Verification 1 0 0 1 1 1 + 0 1 0 1 1 0 + ___ ___________ 128 64 32 16 8 4 2 1 =

5. Octal Addition 1 1 6 4 3 7 8 + 2 5 1 0 8 9 9 - 8 8 (subtract Base (8)) 1 1 1 4 7 8

6. Octal Addition ex 3 5 3 6 8 + 2 4 5 7 8 - (subtract Base (8))

7. Hexadecimal Addition 1 1 7 C 3 9 16 + 3 7 F 2 16 20 18 11 - 16 16 (subtract Base (16)) B 4 2 B 16

8. Hexadecimal Addition 8 A D 4 16 + 5 D 6 16 - (subtract Base (16)) 16

9. Decimal Subtraction 7 13 10 8 4 1 15 - 4 6 5 7 3 7 5 8 How it was done? ( add the base 10 when borrowing) 10 10 7 3 0 10 8 4 1 5 13 10 15 - 4 6 5 7 3 7 5 8

10. Binary Subtraction 1 2 1 0 2 0 2 2 1 0 1 0 0 1 1 - 0 1 1 1 0 0 1 1 0 1 1 1 Verification 83 10 - 28 10 55 10 64 32 16 8 4 2 1 1 1 0 1 1 1 = 32 + 16 + + 4 + 2 +1 = 55 10

11. Binary Subtraction ex Verification 1 0 0 1 1 1 - 0 1 0 1 1 0 - ___ ___________ 128 64 32 16 8 4 2 1 =

12. Octal Subtraction 8 0 0 8 1 1 1 4 7 8 8 9 - 6 4 3 7 8 2 51 0 8

13. Octal Subtraction ex 3 5 3 6 8 - 2 4 5 7 8

14. Hexadecimal Subtraction B 16 7 C 3 9 16 19 - 3 7 F 2 16 4 4 4 7 16

15. Hexadecimal Subtraction 8 A D 4 16 - 5 D 6 16 16