Decimal Number System MCQ Quiz in मल्याळम - Objective Question with Answer for Decimal Number System - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Given:

The number is (111)₂

Calculation:

⇒ 2² × 1 + 2¹ × 1 + 2⁰ × 1 = 4 + 2 + 1 = 7

∴ The required result will be 7.

Concept:

Let a number is represented in a base 'b' number system as b₃ b₂ b₁ b₀

The decimal equivalent of this number will be:

b₃ × 2³ + b₂ × 2² + b₁ × 2¹ + b₀ × 2⁰

We observe that the decimal equivalent will be minimum when the base of the number system 'b' is minimum.

Application:

The given number is 11C.0

The minimum decimal equivalent for this number is possible for a valid minimum base system for this number.

Since the largest digit in the given number is C which is expressed by 12, the minimum valid base will be 13.

∴ The minimum decimal equivalent of the given number will be:

(11 C)₁₃ = 1 × 13² + 1 × 13¹ + 12 × 13⁰

= 169 + 13 + 12

= (194)₁₀

Concept:

For conversion binary to octal number the binary numbers starting from the binary point, groups are made of 3 bits each, on either side of the binary point.

Application:

Binary: 111 101 000

Grouping in 3 digit: 

Octal equivalent: 750

n binary addition,

0 + 0 = 0 without any carry

0 + 1 = 1 without any carry

1 + 0 = 1 without any carry

1 + 1 = 0 with carry 1.

Hence the binary addition of (1101)₂ and (1000)₂ is (10101)₂

Therefore correct answer is Option 3

(1235)_x = (3033)_y

Converting both the RHS and LHS into its decimal equivalent, we get:

(x³ + 2x² + 3x + 5)₁₀ = (3y³ + 0y² + 3y + 3)₁₀

Substituting the values given in the options in above equation, we get:

x = 8 and y = 6

Proof:

Putting x = 8 in x³ + 2x² + 3x + 5

= (8)³ + 2(8)² + 3(8) + 5

= (669)₁₀

Putting y = 6 in 3y³ + 0y² + 3y + 3

= 3(6)³ + 3(6) + 3

= 3(216) + 18 + 3

= (669)₁₀

The correct option is 4

Concept:

Given:

The hexadecimal number is (BC9)₁₆

Concept:

To convert hexadecimal to decimal, the following steps are involved.

1 → Multiply each digit of a hexadecimal number with powers of 16.

2 → These powers should be positive for an integral part and negative for the fractional part.

3 → Add the all multiplying digits

Calculation:

⇒ (BC9)₁₆ = B × 16² + C × 16¹ + 9 × 16⁰

⇒ (BC9)₁₆ = 11 × 256 + 12 × 16 + 9 × 1

⇒ (BC9)₁₆ = 2816 + 192 + 9

⇒ (BC9)₁₆ = (3017)₁₀

∴ The required result will be (3017)₁₀.

Concept:

To convert any number system into the decimal number system, multiply each position by its weight and add.

For example:

\(\begin{array}{*{20}{c}} x\\ \downarrow \\ {{b^2}} \end{array}\;\begin{array}{*{20}{c}} y\\ \downarrow \\ {{b^1}} \end{array}\;\begin{array}{*{20}{c}} z\\ \downarrow \\ {{b^0}} \end{array}\)

Analysis:

(1010)2 = [(1 × 2³) + (0 × 2²) + (1 × 2¹ ) + (0 × 2⁰)]₁₀

= (10)₁₀

(89D)₁₆ = 8 × 16² + 9 × 16¹+ 13 × 16⁰

(89D)16 = 2048+144+13 = (2205)10      

(2205)₁₀ + (259)₁₀ = (2464)₁₀

Option 1:

(9EA)16 = 9 × 162 + 14× 161+ 10 × 160 = (2538)₁₀

Option 2:

(3472)8 =3 × 83 + 4 × 82 + 7 × 81+ 2 × 80 = (1850)10

Option 3:

(2464)10

Therefore it is correct

Option 4:

(63215)8 =6 × 84 + 3 × 83 + 2 × 82 + 1 × 81+ 5 × 80 = (26253)10

Therefore Option 3 is correct.

Binary to Hexadecimal conversion table:

Memory Size are as follows:

Therefore 220 bytes and 240 bytes are respectively equal to 1 MB  and 1 TB