In Memory of George Boole

Number Theory Level 4

Today, November 2, is the 11001000bth birthday of George Boole, from which Boolean Algebra originated. In what year was he born?

1110001010 1 2 11100010101_2 342 6 8 3426_8 211102 1 3 2111021_{3} 71 6 16 716_{16} 0 A 9 9 13 0A99_{13} 140 0 11 1400_{11} None of the choices

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Efren Medallo by Efren Medallo , 26, Philippines

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1 solution

Himanshu Agrawal
Nov 2, 2015

( 11001000 ) 2 = 1 × 2 7 + 1 × 2 6 + 1 × 2 3 = ( 200 ) 10 (11001000)_{2} = 1 \times 2^{7} + 1 \times 2^{6} + 1 \times 2^{3} = (200)_{10}

So, Birthday year is 2015 - 200 =1815

Now, ( 1400 ) 11 = 1 × 1 1 2 + 4 × 11 = ( 1815 ) 10 (1400)_{11} = 1 \times 11^{2} + 4 \times 11 = (1815)_{10}

Therefore, Answer is ( 1400 ) 11 \boxed{(1400)_{11}}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Oh so silly of me. Forgot to calculate birth year.

Shubham Bhargava - 5 years, 7 months ago

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