binary arithmetic rules
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The document discusses various binary operations - addition, subtraction, multiplication, and division. It also covers 1's complement and 2's complement representations of signed binary numbers. Some key points covered include: - Binary addition and subtraction use carry/borrow bits - Multiplication is done by ANDing corresponding bits, division gives the quotient bit - 1's complement is obtained by flipping all bits, 2's complement adds 1 to the 1's complement - Subtraction can be performed using addition with 1's or 2's complement representations - Signed numbers can be represented in sign-magnitude, 1's complement, or 2's complement forms.
binary arithmetic rules
- 1. Binary Addition, Subtraction , Multiplication and division
- 2. Binary addition:- A B Sum Carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 Binary subtraction:- A B Difference Borrow 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 0
- 3. Add the following binary numbers: 1. (1001)2 and (0101)2 2. (101.01)2 and (1101.10)2 Subtract the following binary numbers: 1. (0110)2 from (1010)2 2. (01011)2 from (11011)2
- 4. Binary Multiplication:- A B Output 0 0 0 0 1 0 1 0 0 1 1 1 Binary Division:- A B Output 0 1 0 1 1 1 Division by zero is meaning less
- 5. Solve the following binary multiplication 1. (101)2 and (11)2 2. (1011)2 and (1001)2 Solve the following division 1.(11001) by (101) 2. (110000) by (100)
- 6. 1’s complement:- The 1’s complement of binary number is obtained by changing each 0 to 1 and each 1 to 0. both the numbers complement each other. If one of these number is positive , the other will be negative with same magnitude and vice versa. 2’s complement:- If 1 is added to 1’s complement of a number then it will obtain the 2’s complement of the number.
- 7. Subtraction using 1’s complement a) Subtraction of smaller number from a larger number:- 1. Calculate the 1’s complement of a smaller number. 2. add the 1’s complement to the larger number. 3. If carry comes in the MSB , remove the carry and add it to the result.
- 8. Subtraction using 1’s complement b) Subtraction of larger number from a smaller number:- 1.Calculate 1’s complement of a larger number. 2. Add 1’s complement in smaller number 3. The result will be in 1’s complement form. Calculate 1’s complement of final value and assign –ve sign to the result.
- 9. Advantages of using 1’s complement subtraction 1. This can be easily obtained by simply inverting each bit in the number 2. This subtraction can be done with an binary adder. Thus ,it is useful in arithmetic logic circuits.
- 10. Subtraction using 2’s complement a) Subtraction of smaller number from a larger number:- 1. Calculate the 2’s complement of a smaller number. 2. add the 2’s complement to the larger number. 3. If carry comes in the MSB , discard the carry .
- 11. Subtraction using 2’s complement b) Subtraction of larger number from a smaller number:- 1.Calculate 2’s complement of a larger number. 2. Add 2’s complement in smaller number 3. The result will be in 2’s complement form. Calculate 2’s complement of final value and assign –ve sign to the result.
- 12. Unsigned and signed numbers Unsigned numbers:- Numbers without any positive and negative sign. Represents only magnitude
- 13. Sign magnitude numbers:- In binary number system, both +ve and –ve values are possible. In this , we use 0’s and 1’s to represent every number. The representation of number is known as signed number. 0+ve number 1 -ve number. Eg:- +7=0111 -7=1111 This kind of representation for signed numbers is called as signed magnitude representation.
- 14. Different methods for the representation of binary signed numbers 1. Sign magnitude form 2. 1’s complement form 3. 2’s complment form