Boolean operators
- 1. LECTURE - 3 • Binary Addition • Binary Subtraction • Complements • 1’s Complement • 2’s Complement • Subtraction Using Complements
- 2. BASIC OPERATIONS • ADDITION • SUBTRACTION • MULTIPLICATION • DIVISION
- 3. COMPUTER OPERATIONS • BINARY ADDITION • BINARY SUBTRACTION
- 4. THE FIRST COMPUTER • Covered a whole Room • Separate Functions for Adding, Subtracting, Multiplication and Division
- 5. ELIMINATION OF OPERATIONS • MULTIPLICATION and DIVISION were eliminated • MULTIPLICATION : repeated addition (2 x 4 = 8) , (2+ 2+ 2 + 2 = 8) • DIVISION : repeated subtractions
- 6. TODAY’S COMPUTER • Computations • Addition – (ADDERS) • Subtraction – (SUBTRACTORS)
- 7. BINARY ADDITION LOGIC: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 (1 Carry)
- 8. EXAMPLE 1 0 0 1 1 0 + 1 1 0 1 0 1 1 0 1 1 0 1 1 Carry
- 9. BINARY SUBTRACTION LOGIC: 0 - 0 = 0 0 - 1 = 1 ( Borrow 1) 1 - 0 = 1 1 - 1 = 0
- 10. EXAMPLE 1 1 0 1 0 1 - 0 1 1 0 1 0 0 1 1 0 1 1
- 11. COMPLEMENTS 2 types: • 1’s Complement • 2’s Complement
- 12. 1’S COMPLEMENT PROCEDURE • Change every 0 to 1 and every 1 to 0 EXAMPLE Find 1’s Complement of: ( 1 1 0 0 1 0 1 0 )2
- 13. 2’S COMPLEMENT PROCEDURE 1. Find 1’s Complement: Change every 0 to 1 and every 1 to 0 2. Add 1 to L.S.B
- 14. EXAMPLE Find 2’s Complement of : ( 1 1 0 1 0 1 0 )2
- 15. SOLUTION : ( 1 1 0 1 0 1 0 )2 STEP 1 0 0 1 0 1 0 1 STEP 2 0 0 1 0 1 0 1 + 1 0 0 1 0 1 1 0 LSB
- 16. SUBTRACTION USING COMPLEMENTS SUBTRACTION • MINUEND (1st value) • SUBTRAHEND (2nd value)
- 17. SUBTRACTION USING 1’S COMPLEMENT STEP 1 Take 1’s Complement of Subtrahend STEP 2 Add the result to Minuend STEP 3 Look for end Carry.
- 18. END CARRY • If Carry Exists: Add the carry to LSB of result • If NO Carry: Take 1’s complement of result again and place a –ve sign
- 19. EXAMPLE Subtract: ( 1 1 0 1 0 1 1 - 1 0 1 1 0 1 )2 SOLUTION Minuend: 1 1 0 1 0 1 1 Subtrahend: 0 1 0 1 1 0 1 STEP 1 1’s Complement of Subtrahend 1 0 1 0 0 1 0 STEP 2 Add to Minuend STEP 3 Add end carry to LSB of result.
- 20. SUBTRACTION USING 2’S COMPLEMENT • STEP 1 Take 2’s Complement of Subtrahend • STEP 2 Add the result to Minuend • STEP 3 Look for end Carry.
- 21. END CARRY • If Carry Exists: Drop it • If NO Carry: • Take 2’s complement of result again and • place a –ve sign
- 22. EXAMPLE Subtract: ( 1 1 0 1 0 1 1 - 1 0 1 1 0 1 )2
- 23. ADVANTAGE OF COMPLEMENTS • It Converts Subtraction Process to Addition • Thus, the need for a Subtractor is Eliminated