EGEC 540 Computer Arithmetic Structures Fall 2023 Exercise 1

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EGEC 540

Computer Arithmetic Structures

Fall 2023

Exercise 1

Due Monday, October 2, 11:45 PM

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1. Add +5 and +6 in binary using the signed 1’s complement representation/format. Assume width of 4 bits. Comment on the result and give reasons wherever applicable

2. Repeat problem 1 with a width of 5 bits

3. Add −2 and −6 in binary using the signed 1’s complement representation/format. Assume width of 4 bits. Comment on the result and give reasons wherever applicable

4. Repeat problem 3 with a width of 5 bits

5. Add −2 and −6 in binary using the signed 2’s complement representation/format. Assume width of 4 bits. Comment on the result and give reasons wherever applicable

6. Repeat problem 5 with a width of 5 bits

7. Answer this question in the context of the IEEE 754 format for representing floating point numbers:

I. Give the value of the largest positive normalized number that can be represented in this format. Assume total width of 32 bits.

II. Give the value of the largest positive denormalized number that can be represented in this format. Assume total width of 32 bits.