boolean operators subtractions using 1's complement subtraction using 2's complement

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