Solution - Base conversion

1, 977

1,977

Step-by-step explanation

${(7 B 9)}_{16} = b a s e 10$

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

${(7 B 9)}_{16} = 7 \cdot 16^{2} + 11 \cdot 16^{1} + 9 \cdot 16^{0}$

$7 \cdot 16^{2} + 11 \cdot 16^{1} + 9 \cdot 16^{0} = 1977$

Expand each digit by place value: $7 \cdot 16^{2}$
+ $11 \cdot 16^{1}$
+ $9 \cdot 16^{0}$ . This gives $1, 977$ in base 10.

$\frac{1977}{10} = 197 r e m a \in d e r 7$

$\frac{197}{10} = 19 r e m a \in d e r 7$

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

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

$7 \to 7 \to 9 \to 1 = 1977$

$1977 (b a s e 10) = {(1977)}_{10}$

Repeatedly divide $1, 977$ by $10$ , collect remainders, and read them in reverse to get $1, 977$ .

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