201 9 b 2019_b

011111100011 2 = 3743 8 = 7 E 3 16 = a b c d 10 ‭\large {011111100011‬_2 = ‭3743‬_8 = ‭7E3‬_{16} = abcd_{10} }

Find a × b × c × d a \times b \times c \times d ?


The answer is 0.

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3 solutions

Chew-Seong Cheong
Dec 27, 2018

Base 2 base 8: 011 3 111 7 100 4 011 3 Base 2 base 16: 0111 7 1110 E 0011 3 Base 16 base 10: 7 × 1 6 2 7 + 14 × 1 6 1 E + 3 × 1 6 0 3 = 201 9 10 \begin{array} {lc} \text{Base 2 }\to \text{ base 8:} & \underbrace{011}_3 \underbrace{111}_7 \underbrace{100}_4 \underbrace{011}_3 \\ \text{Base 2 }\to \text{ base 16:} & \underbrace{0111}_7 \ \underbrace{1110}_E \ \underbrace{0011}_3 \\ \text{Base 16 }\to \text{ base 10:} & \overbrace{7 \times 16^2}^7 + \overbrace{14\times 16^1}^E + \overbrace{3\times 16^0}^3 & = 2019_{10} \end{array}

Therefore a × b × c × d = 2 × 0 × 1 × 9 = 0 a\times b \times c \times d = 2 \times 0 \times 1 \times 9 = \boxed 0 .

Jordan Cahn
Dec 27, 2018

01111110001 1 2 = 1024 + 512 + 256 + 128 + 64 + 32 + 2 + 1 = 201 9 10 374 3 8 = 3 ( 512 ) + 7 ( 64 ) + 4 ( 8 ) + 3 = 201 9 10 7 E 3 16 = 7 ( 256 ) + 14 ( 16 ) + 3 = 201 9 10 \begin{aligned} 011111100011_2 &= 1024+512+256+128+64+32+2+1 = 2019_{10} \\ 3743_8 &= 3(512) + 7(64) + 4(8) + 3 = 2019_{10} \\ 7E3_{16} &= 7(256) + 14(16) + 3 = 2019_{10} \end{aligned}

2 × 0 × 1 × 9 = 0 2\times 0\times 1\times 9 = 0

go to this webpage

https://www.tools4noobs.com/online tools/base convert/

and get the answer immediately.

Can you post something interesting once, for the love of god! Some question that people cannot find the answer to so easy.

For the sake of GOD do not solve my problems>>>> hahaha try my other problems!!!

Even with this easy problem you, 10% didn't solve it.

Ossama Ismail - 2 years, 5 months ago

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Try this one ..... https://brilliant.org/problems/can-you-find-your-lost-dog/

Ossama Ismail - 2 years, 5 months ago

Well, this one I solved. So, I don't know what you mean by "you, 10%". The other problem, I had a look at it and it is kinda cool (I made an approximation and got 16.37. BTW, area in which metric or unit?). But, I am talking "number theory" here. You basically change the values of rather known problems and post as new questions.

A Former Brilliant Member - 2 years, 5 months ago

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From time to time I post easy problems. "you , 10%" is a typing mistake. Thanks for your note about the "lost dog problem". I added that area in k m 2 km^2 .

Ossama Ismail - 2 years, 5 months ago

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@Ossama Ismail Best wishes and regards

A Former Brilliant Member - 2 years, 5 months ago

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