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Computer Science: Number Conversion and Logic Circuits

Question
Part A

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Table 1.
1. Please follow the instructions to complete Table 1.
2. Convert the decimal number to octal.
3. Convert the octal number to hexadecimal.
4. Convert the hexadecimal number to binary.
5. Add the two binary numbers.
6. Convert the binary sum to hexadecimal.
7. Convert the hexadecimal number to octal.
8. Convert the Octal number to decimal.
1. Convert the decimal fraction 0.453125 to binary.
2. Convert the binary fraction 0.10000001 to decimal.
3. Convert the octal fraction 0.370 to decimal.
4. Simplify the following Boolean expression:
5. (x + y) z' + y(x' + z')
6. x'z (xy + y'z' + yz)
7. y' (xz' + y'z)'
8. (y + z')' (x' + y)'
4.Using the truth table,prove the following expression
1. (x + y z)' + y' (x y + z) = x' y' +x' z' + y'z
2. (yz' + x'z)' = xy' + xz + y'z'
3. Construct a truth table for R(x,y,z) = x' y + x' z + y' z' and draw the corresponding logic circuits
Part B

You need to develop a special calculator with the following features

1. Add 2 number.
2. Divide 2 number.
3. Multiply 2 number.
4. Modulus of 2 numbers.
5. Convert Decimal to Binary
6. Convert Decimal to Octal
7. Convert Decimal to Hexadecimal
Instructions
1. Produce the pseudocode for each of the features.
2. Write a complete C program that allows the user to choose the feature from a menu and display the result.
3. Each of the feature must be implemented using appropriate C function.
4. Produce test cases for each function that you have developed.