Question

75%20%5C%3A%20%20%29_%7B10%7D%20%5C%3A%20%20into%20%20%5C%3A%20binary%20%5C%3A%20%20equivalent.%20%5C%3A%20" id="TexFormula1" title=" { \green \bigstar}\rm \: Convert \: ( \: 268.75 \: )_{10} \: into \: binary \: equivalent. \: " alt=" { \green \bigstar}\rm \: Convert \: ( \: 268.75 \: )_{10} \: into \: binary \: equivalent. \: " align="absmiddle" class="latex-formula">
Thank uh ~​

Answer 1

$\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}$

Divide 268 by 2, keeping notice of the quotient and the remainder. You will have to keep dividing the quotient by 2 until you get a quotient of zero as shown below:

$\small\longrightarrow \sf{\dfrac{268}{2} =134 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{134}{2} = \: 67 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{67}{2} = \: 33 \: R \: 1 }$

$\small\longrightarrow \sf{\dfrac{33}{2} = \: 16 \: R \: 1}$

$\small\longrightarrow \sf{\dfrac{16}{2} = \: 8 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{8}{2} = \: 4 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{4}{2} = \: 2 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{2}{2} = 1 \: R \: 0}$

$\small\longrightarrow \sf{\dfrac{1}{2} = \: 0 \: R \: 1}$

Writing out the remainder from bottom to top will give 100001100.

Multiply the decimal 0.75 by 2 and keep noting down by integer values as shown:

$\sf\longrightarrow{\small 0.75 \cdot 2 = 1.5 = 1 + 0.5}$

$\sf\longrightarrow{\small 0.5 \cdot 2 = 1.0 = 1 +0}$

The equivalent binary for 0.75 will be 0.11.

▪ $\sf\longrightarrow{100001100 + 0.11 = 100001100.11}$



$\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}$

$\large\boxed{\bm{100001100.11}}$