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CS/EE 3810 Assignment 5 solved

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1. Convert the decimal number -26.3125 into the IEEE 754 format for a single-precision
floating-point number. (20 points)
2. Convert the following IEEE 754 single-precision floating-point register into a decimal
number: 1 10000111 11010000000000000000000. (20 points)
3. Convert the following IEEE 754 double-precision floating-point register into a decimal
number: 1 10000000011
1010000000000000000000000000000000000000000000000000. (20 points)
4. What is the result of adding the following two IEEE 754 single-precision floating-point
registers? Show your steps as you perform the math in binary and produce the final
IEEE 754 value that will be placed in the register. (20 points)
0 10000010 00100000000000000000000
0 10000101 11000000000000000000000
5. Compute the truth table for a logic block that takes in a 3-bit input and produces a 2-
bit output that represents the number of 1’s in the 3-bit input. For example, if the
input is 101, the output should be 10, i.e., there are two 1’s in the input 101. Express
each output bit with a sum-of-product Boolean equation. (20 points)