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Decimal Addition

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. Binary Addition. Rules. 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1

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Decimal Addition

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  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 = 102 = 0 with 1 to carry • 1 + 1 + 1 = 3 = 112 = 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 • 5510 • + 2810 • 8310 • 64 32 16 8 4 2 1 • 1 0 1 0 0 1 1 • = 64 + 16 + 2 +1 • = 8310

  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 78 + 2 5 1 08 9 9 - 8 8 (subtract Base (8)) 1 1 1 4 78

  6. Octal Addition ex 3 5 3 68 + 2 4 5 78 - (subtract Base (8))

  7. Hexadecimal Addition 1 1 7 C 3 916 + 3 7 F 216 20 18 11 - 16 16 (subtract Base (16)) B 4 2 B16

  8. Hexadecimal Addition 8 A D 416 + 5 D 616 - (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) • 1010 • 73010 • 8 41 5131015 • - 4 6 5 7 • 3 7 5 8

  10. Binary Subtraction • Verification • 8310 • - 2810 • 5510 • 64 32 16 8 4 2 1 • 1 1 0 1 1 1 • = 32 + 16 + + 4 + 2 +1 • = 5510 1 2 1 02 0 2 2 1 0 1 0 0 1 1 - 0 1 1 1 0 0 1 1 0 1 1 1

  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 11 4 78 89 - 6 4 3 78 2 5 1 08

  13. Octal Subtraction ex 3 5 3 68 - 2 4 5 78

  14. Hexadecimal Subtraction B 16 7 C 3 916 19 - 3 7 F 216 4 4 4 716

  15. Hexadecimal Subtraction 8 A D 416 - 5 D 616 16

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