1. DAT2343 Arithmetic Circuits For Unsigned Binary Values © Alan T. Pinck / Algonquin College; 2003

2. Addition of 2 Single Bits

3. The Carry Output from 2-Bit Addition

4. The Result Output from 2-Bit Addition

5. Addition of 3 Single Bits

6. The Carry In 3-Bit Addition

7. Operation Time Requirements for a 3-Bit Adder Assuming a 5 nanosecond response/gate switching time for each basic logic gate: It will take 5 nsec. until A is reliably valid; then another 5 nsec. until B is reliably valid; and then another 5 nsec. (total 15 nsec.) until Carry is reliably valid.

8. Adders for Multi-bit Words Example: Addition of Two 3-bit Words 0 1 1 + 1 0 1 ----------

9. Addition of Two 3-bit Words: Step 1 Add the right-most pair of bits, generating a result for position 0 and a carry for the next position

10. Addition of Two 3-bit Words: Step 2 Add the pair of bits in the next position (position 1) and the carry output from position 0.

11. Addition of Two 3-bit Words: The Full Circuit

12. Subtraction of 2 Single Bits

13. Internal Structure of a 2-Bit Subtract Gate

14. 3-Bit Subtraction

15. Multiplication – By 2

16. Multiplication by a Word with All Its Bits “On”

17. Multiplication: The General Binary Case

18. Beyond Multiplication Division is more complex and takes longer to perform than multiplication. Division of integer values (such as unsigned binary) generates 2 results: a quotient and a remainder. Exponentiation and other advanced arithmetic operations are even more complex.

19. End of Lecture