# discrete math

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1. You are to write the proof for

It is not a trivial proof, so follow the technique given in the PowerPoint presentation. Document every step taken, as was done in the PPT.

2. Use another technique to show that De Morgan’s Laws are tautologies. Draw a truth table for both equations. Use the Word table feature, to create tidy neat-appearance truth tables.

3. Give the dual of the following logical expression:

Create truth tables for both the original expression and the dual. Verify and explain how this illustrates that the original expression and the dual are equivalent. (Note: if the original expression is true on the truth table then its dual should be false – and vice versa.)

4. Consider the following expression with minimal parentheses

Add parentheses to reflect the order in which the operations would be performed, according to the precedence of the logic operators.

(Of course) draw the truth table for the expression.

5. Use the Word table feature to list all the possible combinations for 4 input parameters. As was illustrated in the PPT, draw the two versions of the table, with shading.

6. Add these three 6-bit binary numbers: 110011 , 111100 , 011100. You should only add two numbers at a time.

Show your addition procedure by drawing a Word table, putting each bit in a separate table cell. Create an extra row above the top number where you will show the carry bit (if any) from one column to the next.

Add an extra column to the left of the most-significant digit, where you will keep the bit (if any) that overflows the 6-bit field.

Once you have your answer from adding the first two numbers, create another table and add the third number to sum you calculated previously.