A) Convert the following: i) Decimal 45 to binary. ii) Binary 101101 to decimal. b) Define the following terms: i) Bit ii) Byte iii) Character set

Here are the solutions to question 18:

a) Convert the following:

i) Decimal 45 to binary.
To convert decimal 45 to binary, we repeatedly divide by 2 and record the remainders:

$$\begin{align*} 45 \div 2 &= 22 \text{ remainder } 1 \\ 22 \div 2 &= 11 \text{ remainder } 0 \\ 11 \div 2 &= 5 \text{ remainder } 1 \\ 5 \div 2 &= 2 \text{ remainder } 1 \\ 2 \div 2 &= 1 \text{ remainder } 0 \\ 1 \div 2 &= 0 \text{ remainder } 1 \end{align*}$$

Reading the remainders from bottom to top gives the binary equivalent.
The binary representation of decimal 45 is $\boxed{101101_2}$.

ii) Binary 101101 to decimal.
To convert binary 101101 to decimal, we multiply each digit by the corresponding power of 2:

$$\begin{align*} 101101_2 &= (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (0 \times 2^1) + (1 \times 2^0) \\ &= (1 \times 32) + (0 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) \\ &= 32 + 0 + 8 + 4 + 0 + 1 \\ &= 45_{10} \end{align*}$$

The decimal representation of binary 101101 is $\boxed{45_{10}}$.

b) Define the following terms:

i) Bit
A bit is the smallest unit of data in a computer, represented by a binary value of either 0 or 1.

ii) Byte
A byte is a unit of digital information that most commonly consists of eight bits. It is often the smallest addressable unit of memory in computer architectures.

iii) Character set
A character set is a defined list of characters (like letters, numbers, and symbols) that a computer can recognize and process, along with their corresponding numerical codes.

c) Explain three advantages of using binary system in computers.

1. Simplicity and Reliability: The binary system uses only two states (0 and 1), which can be easily represented by electrical signals (on/off, high/low voltage). This makes electronic circuits simpler to design and more reliable in operation.
2. Noise Immunity: The distinct difference between the two states (0 and 1) makes the system highly resistant to electrical noise and interference, ensuring data integrity.
3. Logical Operations: Binary numbers are perfectly suited for implementing Boolean logic (AND, OR, NOT gates), which forms the fundamental basis of all digital computation and decision-making processes within a computer.

d) Differentiate between ASCII and Unicode.

• ASCII (American Standard Code for Information Interchange): An older character encoding standard that uses 7 bits to represent 128 characters, primarily English letters, numbers, and basic symbols. It is limited in its ability to represent characters from other languages.
• Unicode: A modern and comprehensive character encoding standard that aims to represent every character from every language in the world. It uses a variable number of bits (typically 8, 16, or 32 bits per character) to support a vast range of characters, including emojis and symbols.