The problem has multiple parts related to information and communication technology. (iii) Match items from two columns. (iv) Convert a hexadecimal number and a binary number to decimal and find their sum. (v) Write the boolean equation for a given logic circuit.

1. Problem Description

The problem has multiple parts related to information and communication technology.

(iii) Match items from two columns.

(iv) Convert a hexadecimal number and a binary number to decimal and find their sum.

(v) Write the boolean equation for a given logic circuit.

2. Solution Steps

(iii) Matching Items

We need to find the correct matches between the descriptions in Column X and the items in Column Y.

1. Internet and electronic mail was invented to the world by: Tim Berners Lee (S)

2. Automatic Sequence Control Calculator: Mark 1 (T)

3. High level programming languages: Java (P)

4. Punch card concept was invented by: Joseph Jacquard (Q)

5. One of the command line Interface Operating system: UNIX (R)

(iv) Conversion and Summation

We need to convert $FD_{16}$ (hexadecimal) and $10010011_2$ (binary) to decimal and then add them.

Hexadecimal to Decimal:

$FD_{16} = (15 \times 16^1) + (13 \times 16^0) = (15 \times 16) + (13 \times 1) = 240 + 13 = 253$

Binary to Decimal:

$10010011_2 = (1 \times 2^7) + (0 \times 2^6) + (0 \times 2^5) + (1 \times 2^4) + (0 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0) = 128 + 0 + 0 + 16 + 0 + 0 + 2 + 1 = 147$

Sum:

$253 + 147 = 400$

(v) Boolean Equation

We need to write the boolean equation for the given logic circuit. The circuit consists of OR gates and an AND gate and NOT gate (inverter).

Let's break down the circuit step by step:

The first OR gate takes inputs $P$ and $Q$. Its output is $P + Q$.

The second OR gate takes input $R$. The output of $R$ is inverted, resulting in $\overline{R}$. The OR gate takes inputs $P + Q$ and $\overline{R}$. Its output is $(P+Q) + \overline{R}$.

The output $F$ is then equal to $F = (P+Q) + \overline{R}$.

3. Final Answer

(iii)

1-S

2-T

3-P

4-Q

5-R

(iv) 400

(v) $F = (P+Q) + \overline{R}$