Number Systems & Data Representation : MCQs & PYQs with Explanation

Option A

Memory storage refers to devices or media used to store data and programs in a computer.

• Primary memory (Volatile) is directly accessible by the CPU and loses its data when the power is turned off, examples include RAM and cache. 
• Secondary memory (Non-Volatile) stores data permanently, such as hard disks, SSDs, and optical discs.
• Tertiary and offline storage is used for backups and large-scale data storage, including tape drives and external hard drives.

Storage units are used to measure the amount of data in a computer, starting from the smallest unit, a bit, to larger units like Byte, Kilobyte (KB), Megabyte (MB), Gigabyte (GB), and Terabyte (TB).

• Bit → Byte → KB → MB → GB → TB → PB → EB → ZB → YB. Trick “Bharat Ke Modi Gaye Taj Pe Ek Zaruri Yatra”.

Option A

To convert a decimal number to octal, we repeatedly divide the number by 8 and record the remainders.

Option A

We need to check both statements by converting the given numbers into decimal form.
Statement I: (1071)₁₀ = (2057)₈
Convert (2057)₈ into decimal:
(2057)₈ = 2*8³ + 0*8² + 5*8¹ + 7*8⁰
= 2*512 + 0*64 + 5*8 + 7*1
= 1024+0+40+7
= 1071
Therefore, (2057)₈ = (1071)₁₀. Hence, Statement I is TRUE.
Statement II: (1AF)₁₆ = (413)₁₀
In hexadecimal, A = 10 and F = 15.
(1AF)₁₆ = 1*16² + 10*16¹ + 15*16⁰
= 1*256 + 10*16 + 15*1
= 256+160+15
= 431
Therefore, (1AF)₁₆ = (431)₁₀, not (413)₁₀. Hence, Statement II is FALSE.

Option A

Option B

Storage units are used to measure the amount of data in a computer, starting from the smallest unit, a bit, to larger units like byte, kilobyte (KB), megabyte (MB), gigabyte (GB), and terabyte (TB).

• Bit → Byte → KB → MB → GB → TB → PB → EB → ZB → YB. Trick “Bharat Ke Modi Gaye Taj Pe Ek Zaruri Yatra”.

Option B

BCD (Binary Coded Decimal) is a coding system where each decimal digit is represented separately by its 4-bit binary equivalent.
BCD does not convert the entire number into pure binary. Instead, it converts each digit individually.

Option B

CSA stands for Computer Speed Addition. It refers to techniques used in computer arithmetic to perform addition faster, often by reducing the time required to handle carries during binary addition.
By designing circuits that can process sums and carries efficiently, computers can speed up arithmetic operations, which is critical in processors and digital systems.

Option B

In ASCII-7, each character is represented by exactly 7 bits. The decimal ASCII code of uppercase A is given as 65. Since uppercase letters have consecutive ASCII codes, we can calculate the codes of the other letters from their positions relative to A.

Now combine the 7-bit codes in the same order as the word EXAM: 1000101101100010000011001101.

Option B

Convert the binary number to decimal.
(0.11101)₂
=1*2^-1+1*2^-2+1*2^-3+0*2^-4+1*2^-5
=0.5+0.25+0.125+0+0.03125
=0.90625
The decimal form is written as (0.90xy5)₁₀.
Comparing with 0.90625, we get, 0.90xy5 = 0.90625
So the digits must be:

• x = 6
• y = 2

Option A

The repeated division method by 2 is used to convert a decimal (base 10) number into a binary (base 2) number.
Steps:
1. Divide the decimal number by 2.
2. Record the remainder.
3. Use the quotient for the next division by 2.
4. Repeat until the quotient becomes 0.
5. The binary number is formed by reading the remainders from bottom to top.