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Binary Math
11 questions By Tony R. Kuphaldt
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Question 10 of 11
How is it possible to tell that overflow has occurred in the addition of binary numbers, without converting the binary sums to decimal form and having a human being verify the answers?
Reveal answerCheck the sign bit of the answer, and compare it to the sign bits of the addend and augend.
Challenge question: under what condition(s) is overflow impossible? When can we add two binary numbers together and know with certainty that the answer will be correct?
Notes:Later, this concept of overflow checking should be applied to a real circuit, with students designing logic gate arrays to detect the presence of overflow. First, though, they must learn to recognize its presence analytically.
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Question 11 of 11
What is a floating-point number in a digital system?
Reveal answer“Floating-point” numbers are the binary equivalent of scientific notation: certain bits are used to represent the mantissa, another collection of bits represents the exponent, and (usually) there is a single bit representing sign. Unfortunately, there are several different “standards” for representing floating-point numbers.
Notes:Ask your students why computer systems would have need for floating point numbers. What’s wrong with the standard forms of binary numbers that we’ve explored thus far?
