caljuice said:Homework Statement
I want to do 8 + (-2) in binary
Homework Equations
8= 1 0 0 0
2= 0 0 1 0
The Attempt at a Solution
To find the negative of 2 I find the tens complement of it by finding nines complement and +1
7 is the nines complement = 0 1 1 1 and adding 0 0 0 1 = 1 0 0 0
1 0 0 0
+1 0 0 0
----------
1 0 0 0 0
Knocking off the carry I get all zeros. The answer should be six. What am I doing wrong?
Tens complement subtraction in binary is a method used to subtract two binary numbers by converting them into their tens complement form and then performing addition on the numbers. This method is commonly used in computer systems to perform subtraction operations.
In this method, the minuend (number being subtracted from) is first converted into its tens complement by inverting all the bits and adding 1 to the result. The subtrahend (number being subtracted) is then added to the tens complement of the minuend, resulting in a binary sum. The final result is obtained by taking the tens complement of this binary sum.
Tens complement subtraction is used in binary because it allows for the use of a single addition operation to perform subtraction, making it more efficient and faster than traditional subtraction methods. It also allows for the representation of negative numbers in binary without using a separate sign bit.
In Tens complement subtraction, borrowing is handled by adding 1 to the next digit when a borrow is needed. This is because when the minuend is converted to its tens complement, the final digit will always be a 1, ensuring that there is always a 1 available for borrowing.
No, Tens complement subtraction is only applicable for binary numbers. In order to use this method for decimal numbers, they would first need to be converted into binary form. However, this method is not commonly used for decimal numbers due to its complexity and the availability of more efficient algorithms.