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The Basics of Binary Arithmetic Operations

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Explore arithmetic functions like binary addition, subtraction, overflow detection, and BCD addition using HDLs. Learn half adder, full adder, and ripple carry adder concepts.

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The Basics of Binary Arithmetic Operations

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  1. Arithmetic Functions and HDLs Chapter 4

  2. Half adder X +Y ----- CS

  3. Full adder X Y +Z ----- CS

  4. Binary ripple carry adder

  5. Binary subtraction (for unsigned binary number) • 11100 (借位) 10011(被減數) - 1 1110(減數) --------------------------------- 10101(差) -01011(正確差)

  6. Example • Y-X 1000011 + 0101100 ----------------- 1101 1 11 - 0010001 • X=1010100;Y=1000011 • X-Y: 1010100 +0111101(27-Y) ----------------------------- 10010001(X-Y)

  7. Signed binary numbers Eg. -9 Sign-mag. 10001001 Sign-1’s 11110110 Sign-2’s 11110111

  8. S0 C0 FA C1 S B A If S=0, (add) If S=1=C0, (sub)

  9. Example • +6 00000110 +13 00001101 ------------------------------- +19 00010011 • -6 1 1 1 11010 +13 00001101 ------------------------------- +7 00000111 • +6 00000110 -13 1 1 1 10011 ------------------------------ -7 1 1 1 11001 • -6 11111010 -13 11110011 ------------------------------ -19 11101101

  10. Overflow Overflow detection logic for addition and subtraction

  11. Multiplication

  12. B3 B2 B1 B0 A2 A1 A0 ------------------------------------------------------------ 0 A0B0 A0B2 A0B1 A0B C A1B3 A1B2 A1B1 A1B0 A2B3 A2B2 A2B1 A2B0 ------------------------------------------------------------ C6 C5 C4 C3 C2 C1 C0

  13. BCD adder • 4 0100 +5 0101 ------------------------------------------- 9 1001 • 4 0100 +8 1000 --------------------------------------------- 12 1100 +0110 --------------------------------------------- 1 0010 (1) (2)

  14. BCD adder • 8 1000 +9 1001 --------------------------------------------- 17 1 0001 +0110 --------------------------------------------- 1 01 11 (1) (7)

  15. 若加出來大於10 就傳出1 若收到‘1’ 則加6 (0110) S3S2S1S0

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