Solution - Base conversion

186

186

Step-by-step explanation

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

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

${(B A)}_{16} = 11 \cdot 16^{1} + 10 \cdot 16^{0}$

$11 \cdot 16^{1} + 10 \cdot 16^{0} = 186$

Expand each digit by place value: $11 \cdot 16^{1}$
+ $10 \cdot 16^{0}$ . This gives $186$ in base 10.

$\frac{186}{10} = 18 r e m a \in d e r 6$

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

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

$6 \to 8 \to 1 = 186$

$186 (b a s e 10) = {(186)}_{10}$

Repeatedly divide $186$ by $10$ , collect remainders, and read them in reverse to get $186$ .

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