Solution - Base conversion

236

236

Step-by-step explanation

${(E C)}_{16} = b a s e 10$

Identify the source number, source base, and target base before converting through base 10.

${(E C)}_{16} = 14 \cdot 16^{1} + 12 \cdot 16^{0}$

$14 \cdot 16^{1} + 12 \cdot 16^{0} = 236$

Expand each digit by place value: $14 \cdot 16^{1}$
+ $12 \cdot 16^{0}$ . This gives $236$ in base 10.

$\frac{236}{10} = 23 r e m a \in d e r 6$

$\frac{23}{10} = 2 r e m a \in d e r 3$

$\frac{2}{10} = 0 r e m a \in d e r 2$

$6 \to 3 \to 2 = 236$

$236 (b a s e 10) = {(236)}_{10}$

Repeatedly divide $236$ by $10$ , collect remainders, and read them in reverse to get $236$ .

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Base conversion is foundational for computer science, digital systems, and number theory.