Convert it! (Problem 3)

Number Theory Level 2

What is the number 1110 1 2 11101_2 (in base 2) when converted in base 10?


The answer is 29.

B D by B D , 16, Bulgaria

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3 solutions

B D
Mar 20, 2020

Relevant wiki Binary numbers

11101 11101 in Base 2 converted to Base 10 is 29 \boxed{29} .

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Chew-Seong Cheong
Mar 22, 2020

1110 1 2 = 10000 0 2 − 1 1 2 = ( 2 5 − 2 2 − 2 0 ) 10 = ( 32 − 2 − 1 ) 10 = 29 10 11101_2 = 100000_2 - 11_2 = (2^5 - 2^2 - 2^0)_{10} = (32-2-1)_{10} = \boxed{29}_{10}

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The given number in base 10 10 is 1 × 2 0 + 0 × 2 1 + 1 × 2 2 + 1 × 2 3 + 1 × 2 4 = 29 1\times 2^0+0\times 2^1+1\times 2^2+1\times 2^3+1\times 2^4=\boxed {29}

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