Questions

1. Convert decimal number \(23.1875\) into equivalent binary number upto 4 factional positions.
2. Convert decimal number \(170.23\) into equivalent hexadecimal number upto 4 factional positions.
3. Convert decimal number \(81.44\) into equivalent octal number upto 4 factional positions.
4. Convert Ocal number \((255.71)_8\) to decimal number
5. Add \(101010101\) and \(1100100\)
6. Add \(1001010\) and \(1101101\)
7. Subtract \(11101010\) from \(10011101\)
8. Subtract \(10101010\) from \(110101\)
9. Find the complement function of \(Y = \overline{A}B\overline{C} + \overline{A}\overline{B}C\)
10. Simplify the expression \(Y = \overline{(\overline{A} + C)\cdot (B + \overline{D})}\) to one form having only single variables inverted.
11. Simplify the expression \(Y = (A + B)(\overline{A}+C)(B+C)\)
12. Find the truth table of the Boolean expression \(Y = \overline{AB + C + \overline{D}}\)
13. Find the truth table of the Boolean expression \(Y = \overline{(A + B)CD}\)
14. Show the Karnaugh map for product-of-sums of the Boolean expression \(Y = A + BC\overline{D}\).
15. Write the POS form of the Boolean expression \(Y = ACD + \overline{A} BCD\).
16. Draw Karnaugh map of \(Y = F(A,B,C,D)= \prod M(0,1,3,8,9,10,14,15)\)
17. Minimize the Boolean expression using Karnaugh map for \(Y = F(A,B,C ) = \overline{A}~\overline{B}\overline{C} + \overline{A}~\overline{B}C + \overline{A}BC + A\overline{B}C\). Verify the correctness using the Boolean Algebra.
18. Minimize the Boolean expression, \(Y = F(A, B, C, D) = \sum m(1, 2, 8, 9, 10, 12, 13, 14)\)

Answers

1. \((10111.0011)_2\)
2. \((AA.3AE1)_{hex}\)
3. \((121.3412)_8\)
4. \((173.890625)_10\)
5. \(0100001110\)
6. \(010110111\)
7. \(01001101\)
8. \(Y = (A + \overline{B} + C)\cdot(A + B + \overline{C})\)
9. \(Y = A\overline{C} + \overline{B}D\)
10. \(\)
11. \(\)
12. \(\)
13. \(\)
14. \(\)
15. \(\)
16. \(\)
17. \(Y = \overline{A}\overline{B}+\overline{A}C +\overline{B}C\)
18. \(\)

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