The document explains binary operations related to logic gates, particularly focusing on one’s and two’s complement methods for binary subtraction. It provides examples to illustrate finding the complements and performing subtraction using both methods, emphasizing handling carries in the process. Additionally, it includes exercises for practicing the concepts presented.

1. Logic gates and Binary Operations

3. Logic gates
• Three basic logic gates ( AND, OR, Not)

6. One’s Complement
• Change (0) to (1) and (1) to (0)

7. Examples
• Example-1: Find 1’s complement of binary number 10101110.
• Simply invert each bit of given binary number, so 1’s
complement of given number will be 01010001.
• Example-1: Find 1’s complement of binary number 1000000.

8. Two’s Complement (The Negative
Number )
• 2’s complement of a binary number is 1 added to the 1’s
complement of the binary number.

9. Examples
• Find the two’s complement of (00011100 )?
Step 1 : Find the One’s Complement by changing the 1 to 0 and 0 to 1
11100011
Step 2 : Add 1
11100011
1
11100100
+
Result:

10. Subtraction with One’s Complement
• Y = A-B = A(-B)
• Step1: Find the one’s Complement of (B)
• Step 2: Add A and B
• Step 3:
• if there is a carry, remove it from the end of the number add it to the
number , The result will be a Positive value means (+Y) ( A>B)
• if there is NO carry, remove the carry bit from end of the number add take
the on’es complement of the result. The result will be a negative number (-Y)
means (A<B)
•

11. Example -1
• Y= 15 -10
• Subtract (1010)2 from (1111)2

12. Example-2:
• Y = 8-10
• Subtract (1010)2 from (1000)2 using 1’s complement method.

13. Subtraction with Two’s Complement
• Y = A-B = A(-B)
• Step1: Find the Two’s Complement of (B)
• Step 2: Add A and B
• Step 3:
• if there is a carry, Omit it from the number, The result will be a Positive value
means (+Y) ( A>B)
• if there is NO carry, take the Two’s complement of the result. The result will
be a negative number (-Y) means (A<B)
•

14. Exampe-1:
• Y = 15-10
• Subtract (1010)2 from (1111)2 using 2’s complement method.

15. Example-2:
• Y=8-10
• Subtract (1010)2 from (1000)2 using 2’s complement.

16. Exercises
• Find the Subtraction of these numbers using both 1’s complement
and 2’s Complement ? Compare the Results?
• A= 243 , B= 123
•Find
• Y=A-B
• Y=B-A

17. For fun
• Solve these two equations
• A = 12 B= 3 Find
• 1) Find Y=A*B
• 2) Find Y = A/B