Solution - Base conversion

677

677

Step-by-step explanation

${(2 A 5)}_{16} = b a s e 10$

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

${(2 A 5)}_{16} = 2 \cdot 16^{2} + 10 \cdot 16^{1} + 5 \cdot 16^{0}$

$2 \cdot 16^{2} + 10 \cdot 16^{1} + 5 \cdot 16^{0} = 677$

Expand each digit by place value: $2 \cdot 16^{2}$
+ $10 \cdot 16^{1}$
+ $5 \cdot 16^{0}$ . This gives $677$ in base 10.

$\frac{677}{10} = 67 r e m a \in d e r 7$

$\frac{67}{10} = 6 r e m a \in d e r 7$

$\frac{6}{10} = 0 r e m a \in d e r 6$

$7 \to 7 \to 6 = 677$

$677 (b a s e 10) = {(677)}_{10}$

Repeatedly divide $677$ by $10$ , collect remainders, and read them in reverse to get $677$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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