Solution - Base conversion

188

188

Step-by-step explanation

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

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

${(B C)}_{16} = 11 \cdot 16^{1} + 12 \cdot 16^{0}$

$11 \cdot 16^{1} + 12 \cdot 16^{0} = 188$

Expand each digit by place value: $11 \cdot 16^{1}$
+ $12 \cdot 16^{0}$ . This gives $188$ in base 10.

$\frac{188}{10} = 18 r e m a \in d e r 8$

$\frac{18}{10} = 1 r e m a \in d e r 8$

$\frac{1}{10} = 0 r e m a \in d e r 1$

$8 \to 8 \to 1 = 188$

$188 (b a s e 10) = {(188)}_{10}$

Repeatedly divide $188$ by $10$ , collect remainders, and read them in reverse to get $188$ .

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