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23. Perform the following Hexadecimal multiplication:
a. FF × B2 16 b. A22 × E1 16
16
16
Ans. F F A 2 2
x B 2 x E 1
+1 +1 A 2 2
E E +8 +1 +1
+A +A + C C C x
+ 5 5 x 8 E 7 E 2
B 1 4 E
B14E 16 8E7E2 16

D. Higher Order Thinking Skills (HOTS)
1. Explain the process and significance of converting between number systems such as binary to decimal and decimal to binary.
How is this relevant to the functioning of computer systems?
Ans. The conversion between number systems such as binary to decimal and decimal to binary is crucial because it allows us to bridge
the gap between human-friendly representations of numbers and the binary-based data processing of computers. When we
convert a decimal number to binary, we break the number down into powers of 2, which aligns with how computers store and
manipulate data at the hardware level. For example, converting the decimal number 77 to binary involves dividing it by 2 and
storing the remainders, eventually giving us the binary equivalent. Similarly, converting binary to decimal involves multiplying
each binary digit by the corresponding power of 2 and adding the results. This process is vital for tasks such as interpreting
memory addresses or input/output data in systems, where the user might interact with decimal numbers, but the computer
processes everything in binary. Understanding these conversions is essential for programmers and engineers when they need to
work with raw data or manipulate binary files.
2. What is the relationship between the hexadecimal and binary systems and why is hexadecimal preferred over binary for
representing large numbers?
Ans. Hexadecimal (base 16) is a shorthand way of representing binary numbers, as it provides a more compact and readable format
for large binary values. In hexadecimal, each digit represents a group of four binary digits (bits), which is also referred to as a
nibble. For example, the binary number 1111 is represented as F in hexadecimal. The primary reason hexadecimal is preferred
over binary in many applications, such as memory addressing or defining colours on web pages, is because it reduces the
number of digits required. Instead of dealing with long binary strings, hexadecimal allows for a more concise and manageable
representation of large binary values. Additionally, hexadecimal is easier for humans to read and work with, while still being
easily convertible to binary when necessary, making it ideal for tasks that involve a lot of data manipulation and interpretation at
the hardware level.

E. Assertion and reasoning questions.
The following questions consist of two statements – Assertion (A) and Reason (R). Answer these questions by selecting the
appropriate option given below:
a. Both A and R are true and R is the correct explanation of A.
b. Both A and R are true but R is not the correct explanation of A.
c. A is true but R is false.
d. A is false but R is true.
1. Assertion (A): In a decimal odometer, when the 'Units' wheel moves from 9 to 0, the 'Ten' wheel increment by 1.
Reason (R): In a base-10 system, each position represents a power of 10 and a carry-over occurs to the next higher place value
once a digit exceeds 9.
Ans. a. Both A and R are true and R is the correct explanation of A.
2. Assertion (A): Media Access Control (MAC) addresses are represented using hexadecimal numbers.
Reason (R): Transponders in the aviation industry transmit codes using the octal number system.
Ans. b. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. Assertion (A): The aviation industry utilizes the octal number system for transmitting codes via transponders.
Reason (R): The octal number system is used as a shorthand for representing file permissions on UNIX systems.
Ans. b. Both (A) and (R) are true but (R) is not the correct explanation of (A).

System of Numeration 49