Converting between binary, octal and hexadecimal systems | Algebra - Number System

Answer: 31

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Explanation :

We know, 2² = 4.

∴ In the number 1101 make pairs of 2 digits starting from right and write them in base 10.

11    01
P₂    P₁

P₁: (01)₂ = 1.

P₂: (11)₂ = 3.

∴ The final answer is (1101)₂ = (31)₄.

Hence, 31.

Answer: 15

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Explanation :

We know, 2³ = 8.

∴ In the number 1101 make pairs of 3 digits starting from right and write them in base 10.

 1    101
P₂    P₁

P₁: (101)₂ = 5.

P₂: (1)₂ = 1.

∴ The final answer is (1101)₂ = (15)₈.

Hence, 15.

Answer: 353

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Explanation :

We know, 2⁴ = 16.

∴ In the number 1101010011 make pairs of 4 digits starting from right and write them in base 10.

11    0101    0011
P₃     P₂       P₁

P₁: (0011)₂ = 3.

P₂: (0101)₂ = 5.

P₃: (11)₂ = 3.

∴ The final answer is (1101010011)₂ = (353)₁₆.

Hence, 353.

Answer: 1001

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Explanation :

We know, 2² = 4.

Convert each digit of the number in base 2 and write it 2-digit format.

  2     1
10    01

∴ (21)₄ = (1001)₂.

Hence, 1001.

Answer: 10001

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Explanation :

We know, 2³ = 8.

Convert each digit of the number in base 2 and write it 3-digit format.

   2       1
010    001

∴ (21)₈ = (10001)₂.

Hence, 10001.

Answer: 100001

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Explanation :

We know, 2⁴ = 16.

Convert each digit of the number in base 2 and write it 4-digit format.

    2         1
0010    0001

∴ (21)₁₆ = (100001)₂.

Hence, 10001.

Answer: Option B

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Explanation :

We know, 2⁴ = 16.

Convert each digit of the number in base 2 and write it 4-digit format.

Here, A = 10, B = 11 and C = 12

   10        11       12
1010    1011    1100

∴ (ABC)₁₆ = (101010111100)₂.

Hence, option (b).

Answer: 1010000

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Explanation :

We know, 2⁴ = 16.

Convert each digit of the number in base 2 and write it 4-digit format.

    5         0
0101    0000

∴ (50)₁₆ = (1010000)₂.

Hence, 1010000.

Answer: 61

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Explanation :

We know, 5² = 25.

∴ In the number 1101 make pairs of 2 digits starting from left and write them in base 10.

11     01
P₂    P₁

P₁: (01)₅ = 1.

P₂: (11)₅ = 6.

∴ The final answer is (1101)₅ = (61)₂₅.

Hence, 61.

Answer: 132000

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Explanation :

We know, 6² = 36.

Convert each digit of the number in base 6 and write it in 2-digit format.

 9     12     0
13    20    00

∴ (9C0)¹⁶ = (132000)₂.

Hence, 132000.