Matching Decimal Numbers to Binary and Communication Types

The question asks us to match items from two lists: List-I containing decimal numbers and communication methods, and List-II containing binary numbers and communication characteristics. Let's analyze each item in List-I and find its correct match in List-II.

Converting Decimal Numbers to Binary

To match the decimal numbers to their binary equivalents, we need to perform decimal-to-binary conversion. We can do this by repeatedly dividing the decimal number by 2 and noting the remainders. The binary number is formed by reading the remainders from bottom to top.

Converting 50 in Decimal to Binary

Let's convert the decimal number 50:

• $50 \div 2 = 25$ remainder $0$
• $25 \div 2 = 12$ remainder $1$
• $12 \div 2 = 6$ remainder $0$
• $6 \div 2 = 3$ remainder $0$
• $3 \div 2 = 1$ remainder $1$
• $1 \div 2 = 0$ remainder $1$

Reading the remainders from bottom up, we get $110010$. Looking at List-II, option (i) is $0110010$. A leading zero does not change the value of a binary number, so $0110010$ is the same as $110010$. Therefore, 50 in decimal matches $0110010$ in binary.

Match: A) 50 in decimal → i) 0110010 in binary

Converting 102 in Decimal to Binary

Now let's convert the decimal number 102:

• $102 \div 2 = 51$ remainder $0$
• $51 \div 2 = 25$ remainder $1$
• $25 \div 2 = 12$ remainder $1$
• $12 \div 2 = 6$ remainder $0$
• $6 \div 2 = 3$ remainder $0$
• $3 \div 2 = 1$ remainder $1$
• $1 \div 2 = 0$ remainder $1$

Reading the remainders from bottom up, we get $1100110$. Looking at List-II, option (ii) is $1100110$. Therefore, 102 in decimal matches $1100110$ in binary.

Match: B) 102 in decimal → ii) 1100110 in binary

Understanding Communication Types

The next part of the question involves matching communication methods with their types: synchronous or asynchronous.

Synchronous Communication

Synchronous communication happens in real-time. It requires both the sender and the receiver to be actively participating at the same moment. Examples include phone calls, video conferences, and live chat.

List-I item C is Real - Time video conferencing. This is a classic example of communication where participants interact live, making it synchronous.

Match: C) Real - Time video conferencing → iii) Synchronous communication

Asynchronous Communication

Asynchronous communication does not require the sender and receiver to be present simultaneously. Messages are sent and received at different times, and there might be a delay between sending a message and receiving a response. Examples include email, SMS texting, and forum posts.

List-I item D is SMS texting. When you send an SMS, the recipient reads it later, and they reply when they are available. This delay characterizes asynchronous communication.

Match: D) SMS texting → iv) Asynchronous communication

Summary of Matches

Based on our analysis, the correct matches are:

• A) 50 in decimal → i) 0110010 in binary
• B) 102 in decimal → ii) 1100110 in binary
• C) Real - Time video conferencing → iii) Synchronous communication
• D) SMS texting → iv) Asynchronous communication

Let's present this in a table format:

This set of matches corresponds to the option A-i, B-ii, C-iii, D-iv.

Revision Table: Key Concepts Review

Additional Information: Decimal to Binary Conversion Steps

The process of converting a decimal integer to binary is fundamental in computer science. Here is a detailed breakdown of the method used:

1. Start with the decimal integer.
2. Divide the number by 2.
3. Note down the remainder (which will be either 0 or 1). This remainder is the least significant bit (LSB) of the binary number.
4. Take the quotient from the division and repeat steps 2 and 3 with the new quotient.
5. Continue dividing by 2 until the quotient becomes 0.
6. Collect all the remainders in the order they were generated, from the last remainder (most significant bit, MSB) to the first remainder (LSB). This sequence of remainders is the binary representation of the decimal number.

For example, converting 13 to binary:

• $13 \div 2 = 6$ R 1
• $6 \div 2 = 3$ R 0
• $3 \div 2 = 1$ R 1
• $1 \div 2 = 0$ R 1

Reading remainders from bottom up: 1101. So, 13 in decimal is 1101 in binary.