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

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

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.

Option C

An eight-bit byte can represent 2⁸ different combinations. Therefore, an eight-bit byte is capable of representing 256 different characters.

Option C

Computers store signed integers (positive and negative) using various representations such as Sign-Magnitude, 1's Complement, and 2's Complement. 
Among these, 2's Complement Representation is the most widely used because it simplifies arithmetic operations and provides a unique representation for zero.
In an 8-bit 2's Complement System:

• The leftmost bit (MSB) is the sign bit.
• If MSB is 0, the number is positive.
• If MSB is 1, the number is negative.

The range of numbers that can be represented is -2^n-1 to (2^n-1-1), i.e., -128 to +127. 
This means that the smallest number that can be represented in an 8-bit 2's complement system is -128, and the largest number is +127.
Given Register Content is 10000000. Since MSB is 1, the number is negative.
Using 2's Complement Conversion:

• Given: 10000000

To find its magnitude:
Step 1: Take the 1's Complement

• Invert all bits of 10000000 = 01111111

Step 2: Add 1

• 01111111 + 00000001 = 10000000

This gives a magnitude of 128.
Since the original number had MSB is 1, the number is negative. Therefore, -128.

Option B

Option C

To convert the hexadecimal number (1F.01B)₁₆ into its decimal equivalent, we first separate it into the integer part (1F) and the fractional part (.01B).

In integer part conversion, each digit is multiplied by 16 raised to the power of its position from right to left, starting with 0.
(1F)₁₆ = 1⋅16¹+F⋅16⁰ = 16+15 = 31
In fractional part conversion, each digit after the hexadecimal point is multiplied by 16 raised to a negative power corresponding to its position.
0⋅16⁻¹+1⋅16⁻²+B⋅16⁻³ = 0 + 0.00390625 + 0.002685546875 = 006591796875 ≈ 0.0065918
After combining integer and fractional parts, 31 + 0.0065918 = 31.0065918
 

Option D

Data in computers is stored in binary form as bits (0 or 1), which are the smallest possible units. The hierarchy is starting from Bits → Nibble → Byte → KB → MB → GB → TB → PB.

However, among the given options (KB, GB, Byte, Nibble), the smallest unit is the Nibble (4 bits), which is smaller than a byte (8 bits).

Option A

To convert a hexadecimal number to binary, convert each hexadecimal digit separately into its 4-bit binary equivalent.

Therefore,
(7C59)₁₆ = (0111 1100 0101 1001)₂

Option D

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”.