Analyzing Incorrect Results in Binary Subtraction

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SUMMARY

The discussion focuses on the challenge of finding two 4-bit binary numbers that yield incorrect results for both unsigned and signed binary subtraction. The user seeks to understand the conditions under which both representations produce erroneous outputs. Key insights reveal that the signed case can be incorrect when the result exceeds the positive range of 4-bit signed integers, while the unsigned case can be incorrect when the result exceeds the maximum value of 4-bit unsigned integers. The user requests a general expression of these conditions.

PREREQUISITES
  • Understanding of 4-bit binary representation
  • Knowledge of signed and unsigned binary arithmetic
  • Familiarity with binary subtraction rules
  • Basic concepts of overflow in binary operations
NEXT STEPS
  • Research the rules of binary subtraction for both signed and unsigned integers
  • Explore the concept of overflow in binary arithmetic
  • Learn about 4-bit signed integer representation and its limits
  • Investigate examples of binary arithmetic errors in digital circuits
USEFUL FOR

This discussion is beneficial for computer science students, software engineers, and anyone interested in understanding binary arithmetic and its implications in digital systems.

btbam91
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I am asked to come up with two 4-bit binary numbers, that when subtracted, provide the wrong result for both the unsigned and signed cases, inspecting only the first 4 bits of the output.

I have come up with numerous combination where the unsigned is correct, the signed is wrong, and vice versa. But I can't get both of them to be wrong!

Thank you for the help!
 
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Can you express the conditions that the operation gets the wrong result, in general terms, for each case?
 

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