Solution - Base conversion

1, 990

1,990

Step-by-step explanation

${(7 C 6)}_{16} = b a s e 10$

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

${(7 C 6)}_{16} = 7 \cdot 16^{2} + 12 \cdot 16^{1} + 6 \cdot 16^{0}$

$7 \cdot 16^{2} + 12 \cdot 16^{1} + 6 \cdot 16^{0} = 1990$

Expand each digit by place value: $7 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $6 \cdot 16^{0}$ . This gives $1, 990$ in base 10.

$\frac{1990}{10} = 199 r e m a \in d e r 0$

$\frac{199}{10} = 19 r e m a \in d e r 9$

$\frac{19}{10} = 1 r e m a \in d e r 9$

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

$0 \to 9 \to 9 \to 1 = 1990$

$1990 (b a s e 10) = {(1990)}_{10}$

Repeatedly divide $1, 990$ by $10$ , collect remainders, and read them in reverse to get $1, 990$ .

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