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. 1âs complement:- The 1âs 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. 2âs complement:- If 1 is added to 1âs complement of a number then it will obtain the 2âs complement of the number.
- 7. Subtraction using 1âs complement a) Subtraction of smaller number from a larger number:- 1. Calculate the 1âs complement of a smaller number. 2. add the 1âs complement to the larger number. 3. If carry comes in the MSB , remove the carry and add it to the result.
- 8. Subtraction using 1âs complement b) Subtraction of larger number from a smaller number:- 1.Calculate 1âs complement of a larger number. 2. Add 1âs complement in smaller number 3. The result will be in 1âs complement form. Calculate 1âs complement of final value and assign âve sign to the result.
- 9. Advantages of using 1âs 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 2âs complement a) Subtraction of smaller number from a larger number:- 1. Calculate the 2âs complement of a smaller number. 2. add the 2âs complement to the larger number. 3. If carry comes in the MSB , discard the carry .
- 11. Subtraction using 2âs complement b) Subtraction of larger number from a smaller number:- 1.Calculate 2âs complement of a larger number. 2. Add 2âs complement in smaller number 3. The result will be in 2âs complement form. Calculate 2âs complement of final value and assign âve sign to the result.
- 12. Unsigned and signed numbers Unsigned numbers:- ďNumbers without any positive and negative sign. ďRepresents only magnitude
- 13. Sign magnitude numbers:- ďIn binary number system, both +ve and âve values are possible. ďIn this , we use 0âs and 1âs to represent every number. The representation of number is known as signed number. 0ď +ve number 1ď -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. 1âs complement form 3. 2âs complment form