2008

1) Show that $(A+B) \cdot(\bar{A}+C)=(A+B+C) \cdot(A+B+\bar{C})$ $(\bar{A}+B+C) \cdot(\bar{A}+\bar{B}+C)$.

Represent right-hand side using NOR gates only.

[10M]

2) (i) Add binary number 110100.01 and 101111.11 (ii) Subtract $\frac{1}{2}$ from $10000{2}$ (iii) Multiply $1100110.01,$ with $1000.1{2}$ (iv) Divide $11101,$ by $1100{2}$ (v) Convert $72905{10}$ to hexadecimal.

[10M]

3) Draw a flow chart and write a program to solve the non-linear equation $e^{x}=4 \sin x$ near the root $\mathrm{x}=\mathrm{x}_{0}$. Calculate the root correct to five decimal places.

[14M]

2007

1) Multiply \(1.01_{2}\) with \(10.1_{2}\).

[5M]

2) Draw a diagram of digital circuit for the function \(F ( X , Y , Z ) YZ + XZ\) using NAND gate only.

[5M]

2006

1) Covert 239870 decimal to - (i)(1)Octal number, (i)(2)Hexadecimal number.

[5M]

2) Evaluate the following expressions bitwise (i)78 OR 87 (ii)78 XR 87 (iii)78 AND 87

[5M]

2005

1) Evaluate the following expressions:
(i) 78 OR 87
(ii) \(78 \times 0 R 87\)
(iii) \(78\) AND 87
(iv) Shift 87 left by 2
(v) Rotate 78 right by 2

[10M]