Q1
(215)7
Answer: 110
Given number is in base 7.
∴ (215)7 = 2 × 72 + 1 × 71 + 5 × 70.
= 98 + 7 + 5 = 110.
Hence, 110.
Converting to decimal system
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Convert the following numbers to decimal system
Type 0 if such a number is not possible.
Q2
TYPE IN THE ANSWER
(111001)2
Answer: 57
Given number is in base 2.
∴ (111001)2 = 1 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20.
= 32 + 16 + 8 + 0 + 0 + 1 = 57.
Hence, 57.
Q3
TYPE IN THE ANSWER
(215)16
Answer: 533
Given number is in base 16.
∴ (215)16 = 2 × 162 + 1 × 161 + 5 × 160.
= 512 + 16 + 5 = 533.
Hence, 533.
Q4
TYPE IN THE ANSWER
(102)3
Answer: 11
Given number is in base 3.
∴ (102)3 = 1 × 32 + 0 × 31 + 2 × 30.
= 9 + 0 + 2 = 11.
Hence, 11.
Q5
TYPE IN THE ANSWER
(104)4
Answer: 0
Given number is in base 4.
In base 4, highest digit that would be possible is 3.
∴ (104)4 number is not possible.
Hence, 0.
Q6
TYPE IN THE ANSWER
(2C01)16
Answer: 11265
Given number is in base 16.
Here, A = 10, B = 11, C = 12 and so on.
∴ (2C05)16 = 2 × 163 + 12 × 162 + 0 × 161 + 1 × 160.
= 8192 + 3072 + 0 + 1 = 11265.
Hence, 11265.
Q7
TYPE IN THE ANSWER
(11111)5
Answer: 781
Given number is in base 5.
∴ (111111)5 = 1 × 54 + 1 × 53 + 1 × 52 + 1 × 51 + 1 × 50.
= 625 + 125 + 25 + 5 + 1 = 781
Hence, 781.
Q8
TYPE IN THE ANSWER
(11111111111)2
Answer: 2047
Given number is in base 2.
∴ (11111111111)2
= 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20.
= 210 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 22 + 21 + 20
= 211 – 1 = 2047
Hence, 2047.
Q9
TYPE IN THE ANSWER
(215)9
Answer: 176
Given number is in base 9.
∴ (215)9 = 2 × 92 + 1 × 91 + 5 × 90.
= 162 + 9 + 5 = 176.
Hence, 176.
Q10
TYPE IN THE ANSWER
(10046)5
Answer: 0
Given number is in base 5.
In base 4, highest digit that would be possible is 3.
∴ (10046)5 number is not possible.
Hence, 0.