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Digital Circuits for. Binary Arithmetic. R. M. M. Oberman. Professor in Information Engineering. Technical University. Delft, The Netherlands. M.
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We can perform the addition of these two numbers, which is similar to the addition of two unsigned binary numbers. But, if the resultant sum contains carry out from sign bit, then discard ignore it in order to get the correct value. If resultant sum is positive, you can find the magnitude of it directly. The resultant sum contains 5 bits.

So, there is no carry out from sign bit. So, the magnitude of sum is 11 in decimal number system.

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Therefore, addition of two positive numbers will give another positive number. The resultant sum contains 6 bits. In this case, carry is obtained from sign bit. So, we can remove it. Therefore, addition of two negative numbers will give another negative number. Have your students do some of these problems on the board, in front of class for all to see.

Binary Arithmetic

Ask them why we do what we do with that bit, when we would usually place it in our answer. Follow-up question: Why are some of these answers incorrect? Hint: perform the additions in decimal form rather than binary form, and then explain why those answers are not represented in the binary answers.

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This question introduces students to the phenomenon of overflow. This is a very important principle to understand, because real computer systems must deal with this condition properly, so as not to output incorrect answers! 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? Check 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?

Digital circuits for binary arithmetic

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. Ask your students why computer systems would have need for floating point numbers. Load More Articles. Worksheet Topics.

Question 1. Question 2. Question 3. I challenged his belief by applying some Socratic irony: Me: How do you use a hand calculator to determine the circumference of a circle, given its diameter? For example, a circle with a diameter of 5 feet has a circumference of. Me: Does a calculator give you the correct answer?

Him: Of course it does.


Me: Does an electronic calculator use decimal numbers, internally, to do math? Him: No, it uses binary numbers, because its circuitry is made up of logic gates.

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Oh, now I see! If the type of number system mattered in doing math, digital computers and calculators would arrive at different answers for arithmetic problems than we would doing the math by hand! Question 4.

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Question 5. Notes: The point about word-length is extremely important.

Question 6. Question 7. Question 8.