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If you have a 600 digit number with only 0's and 1's, and exactly 300 1's, can the number be a square?

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I am trying to undersatnd why you say the answer is No. for a 6 bit binary number, of which 3 bits are exactly 1s. 25 and 49 are possible such numbers that happens to be a square... Why can't this possibility extend to a 600 bit binary number?

The answer should be YES: @gustion: your example with 49 (7 pwr2) is correct but with 25 (5 pwr2) is incorrect. 7 in binary is 111 (3 1-bits is half of 6 bits), but 5 in binary is 101 (2 1-bits does not equal half of 6 bits). In general, any binary number with n-bits, half of which are 0's and half are 1's is a square of a binary number with half the number of bits, all being 1-value bits. In addition, the number's magnitude will be n/2-1 1-bits followed by n/2 0-bits followed by the last 1-bit. For example, lets say we have a 16-bit number. The number which will have 8 1-bit and 8 0-bit binary digits and also be a square is: 1111 1110 0000 0001 (7 1-bits followed by 8 0-bits followed by 1-bit) and this number is a square of 1111 1111 Binary number with 600 bits and 300 1-bits will have a magnitude of 299 1-bits followed by 300 0-bits followed by 1-bit, and it will be a square of a 300-bit number with the magnitude of 300 1-bits.

Please discuss the differences between USB 2.0 and USB 3.0

1 Answer

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1 Answer

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1 Answer

Are you open to learning?

1 Answer

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What kind of obstacles did you encounter at your work place, and how did you resolve it?

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