any-one-can-explain-me-how-to-change-decimal-number-to-biner-number-i-m-forgot-example-315-10-2-thank-you-

Question Number 113134 by bemath last updated on 11/Sep/20

any one can explain me how to

change decimal number to

biner number . i^{'} m forgot .

example {(315)}_{10} = {(\dots)}_{2}

thank you

Commented by I want to learn more last updated on 11/Sep/20

2 315 Remainder

- - - - ∣ - - - - - ∣ - - - - - - - -

2 ∣ 157 ∣ 1

2 ∣ 78 ∣ 1

2 ∣ 39 ∣ 0

2 ∣ 19 ∣ 1

2 ∣ 9 ∣ 1

2 ∣ 4 ∣ 1

2 ∣ 2 ∣ 0

2 ∣ 1 ∣ 0

2 ∣ 0 ∣ 1

read the remainder from bottom to top

315_{10} = 100111011_{2}

Commented by bemath last updated on 11/Sep/20

thank you friend

Answered by MJS_new last updated on 11/Sep/20

find the largest n with 2^{n} ⩽ 315

\Rightarrow n = 8

{(315)}_{10} = {(1 \underset{7}{a} \underset{6}{a} \underset{5}{a} \underset{4}{a} \underset{3}{a} \underset{2}{a} \underset{1}{a} \underset{0}{a})}_{2}

315 - 2^{8} = 59

find the largest n with 2^{n} ⩽ 59

\Rightarrow n = 5

{(315)}_{10} = {(1001 \underset{4}{a} \underset{3}{a} \underset{2}{a} \underset{1}{a} \underset{0}{a})}_{2}

59 - 2^{5} = 27

\dots

Commented by bemath last updated on 11/Sep/20

thank you prof

Answered by mr W last updated on 11/Sep/20

⌊ \log_{2} 315 ⌋ = 8

315 - 2^{8} = 59

⌊ \log_{2} 59 ⌋ = 5

59 - 2^{5} = 27

⌊ \log_{2} 27 ⌋ = 4

27 - 2^{4} = 11

⌊ \log_{2} 11 ⌋ = 3

11 - 2^{3} = 3

⌊ \log_{2} 3 ⌋ = 1

3 - 2^{1} = 1 = 2^{0}

\Rightarrow 315 = 2^{8} + 2^{5} + 2^{4} + 2^{3} + 2^{1} + 2^{0}

= 1 \times 2^{8} + 0 \times 2^{7} + 0 \times 2^{6} + 1 \times 2^{5} + 1 \times 2^{4} + 1 \times 2^{3} + 0 \times 2^{2} + 1 \times 2^{1} + 1 \times 2^{0}

= {(100111011)}_{2}

Commented by bemath last updated on 11/Sep/20

thank you prof

Answered by Aziztisffola last updated on 11/Sep/20

Commented by bemath last updated on 11/Sep/20

thank you friend

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