Solution - Base conversion

1, 524

1,524

Step-by-step explanation

${(5 F 4)}_{16} = b a s e 10$

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

${(5 F 4)}_{16} = 5 \cdot 16^{2} + 15 \cdot 16^{1} + 4 \cdot 16^{0}$

$5 \cdot 16^{2} + 15 \cdot 16^{1} + 4 \cdot 16^{0} = 1524$

Expand each digit by place value: $5 \cdot 16^{2}$
+ $15 \cdot 16^{1}$
+ $4 \cdot 16^{0}$ . This gives $1, 524$ in base 10.

$\frac{1524}{10} = 152 r e m a \in d e r 4$

$\frac{152}{10} = 15 r e m a \in d e r 2$

$\frac{15}{10} = 1 r e m a \in d e r 5$

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

$4 \to 2 \to 5 \to 1 = 1524$

$1524 (b a s e 10) = {(1524)}_{10}$

Repeatedly divide $1, 524$ by $10$ , collect remainders, and read them in reverse to get $1, 524$ .

Was this explanation helpful?

How did we do?

Learn more with Tiger

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