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Numbers

Converting values between decimal, binary, hexadecimal and other bases, and spotting impossible representations by their digits alone.

A Cool Brisk Walk Through Discrete Mathematics, Numbers

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30 exercises

Exercise 1

If I told you that the decimal number (i.e., base-10 number) 2022 was equal to $13621_6$ , would you call me a liar without even having to think too hard?

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Exercise 2

If I told you that the decimal number 2022 was equal to $1413_6$ , would you call me a liar without even having to think too hard?

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Exercise 3

If I told you that the decimal number 2022 was equal to 8FA $8_{16}$ , would you call me a liar without even having to think too hard?

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Exercise 4

If I told you that the decimal number 2022 was equal to 1231 $0_{6}$ , would you call me a liar without even having to think too hard?

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Exercise 5

If I told you that the decimal number 2022 was equal to 7E $6_{16}$ , would you call me a liar without even having to think too hard?

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Exercise 6

If I told you that 98,243,917,215 mod 7 was equal to 1, would you call me a liar without even having to think too hard?

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Exercise 7

If I told you that 273,111,999,214 mod 6 was equal to 6, would you call me a liar without even having to think too hard?

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Exercise 8

Are the numbers 18 and 25 equal?

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Exercise 9

Are the numbers 18 and 25 congruent mod 7?

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Exercise 10

Are the numbers 18 and 25 congruent mod 6?

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Exercise 11

Are the numbers 617,418 and 617,424 equal?

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Exercise 12

Are the numbers 617,418 and 617,424 congruent mod 3?

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Exercise 13

Are the numbers 617,418 and 617,424 congruent mod 2?

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Exercise 14

Are the numbers 617,418 and 617,424 congruent mod 5?

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Exercise 15

Are the numbers 617,418 and 617,424 congruent mod 6?

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Exercise 16

What's $1_{16} + 2_{16}$ ?

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Exercise 17

What's $1_{16} + 9_{16}$ ?

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Exercise 18

What's $1_{16} + \textrm{E}_{16}$ ?

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Exercise 19

What's $1_{16} + \textrm{F}_{16}$ ?

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Exercise 20

What's $11_{16} + 22_{16}$ ?

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Exercise 21

What's $11_{16} + 99_{16}$ ?

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Exercise 22

What's $11_{16} + \textrm{EE}_{16}$ ?

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Exercise 23

What's $11_{16} + \textrm{EF}_{16}$ ?

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Exercise 24

What's the binary number $1011001110101010_2$ in hexadecimal? Or is that too hard a question to eyeball?

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Exercise 25

What's the binary number $1011001110101010_2$ in decimal? Or is that too hard a question to eyeball?

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Exercise 26

What's the hex number F4CE $_{16}$ in decimal? Or is that too hard a question to eyeball?

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Exercise 27

What's the hex number F4CE $_{16}$ in binary? Or is that too hard a question to eyeball?

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Exercise 28

If I told you that the bit pattern 1010 was meant to represent an unsigned number, what value would it represent?

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Exercise 29

If I told you that the bit pattern 1010 was meant to represent a sign-magnitude number, what value would it represent?

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Exercise 30

If I told you that the bit pattern 1010 was meant to represent a two's-complement number, what value would it represent?

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