I do not understand why the following subtraction method of unsigned integers actually works. A-B 9-3 1001-0011. 1. Switching bits in B 1100. 2. Adding 1 to B 1101. Call this BC. 2... I do not understand why the following subtraction method of unsigned integers actually works. A-B 9-3 1001-0011. 1. Switching bits in B 1100. 2. Adding 1 to B 1101. Call this BC. 2. Adding them together A+BC 1001+1101=0110=6. But why does this work?
Understand the Problem
The question is asking for an explanation of why a specific method of unsigned integer subtraction works. It describes a process involving bit manipulation and addition, seeking further clarity on the underlying principles behind this method.
Answer
Using the two's complement method, 1001 - 0011 can be calculated by adding 1001 and the two's complement of 0011, resulting in 0110 (6).
The subtraction works by using the two's complement method, which allows subtracting B by effectively adding the negative of B using its complement representation.
Answer for screen readers
The subtraction works by using the two's complement method, which allows subtracting B by effectively adding the negative of B using its complement representation.
More Information
Using two's complement is a fundamental approach in computer arithmetic for simplifying the hardware to handle subtraction by converting it into an addition problem.
Tips
Ensure to handle the binary carry properly when adding the complemented binary numbers.
Sources
- Unsigned Integer Binary Subtraction - Mathematics Stack Exchange - math.stackexchange.com
- Lecture notes - Chapter 6 - Integer Arithmetic - cs.wisc.edu - pages.cs.wisc.edu
- Is unsigned integer subtraction defined behavior? - Stack Overflow - stackoverflow.com
