Solution - Base conversion

1, 988

1,988

Step-by-step explanation

${(7 C 4)}_{16} = b a s e 10$

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

${(7 C 4)}_{16} = 7 \cdot 16^{2} + 12 \cdot 16^{1} + 4 \cdot 16^{0}$

$7 \cdot 16^{2} + 12 \cdot 16^{1} + 4 \cdot 16^{0} = 1988$

Expand each digit by place value: $7 \cdot 16^{2}$
+ $12 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $1, 988$ in base 10.

$\frac{1988}{10} = 198 r e m a \in d e r 8$

$\frac{198}{10} = 19 r e m a \in d e r 8$

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

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

$8 \to 8 \to 9 \to 1 = 1988$

$1988 (b a s e 10) = {(1988)}_{10}$

Repeatedly divide $1, 988$ by $10$ , collect remainders, and read them in reverse to get $1, 988$ .

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