Conversion from Hexadecimal to Binary/Examples/6C5

Example of Conversion from Hexadecimal to Binary

The integer expressed in hexadecimal as $6 \mathrm C 5_H$ can be expressed in binary as:

$6 \mathrm C 5_H = 110 \, 1100 \, 0101_2$

Proof

Each of the hexadecimal digits $6$, $\mathrm C$ and $5$ can be expressed in binary as:

\(\ds 6_H\)

\(=\)

\(\ds 0110_2\)

\(\ds \mathrm C_H\)

\(=\)

\(\ds 1100_2\)

\(\ds 5_H\)

\(=\)

\(\ds 0101_2\)

Hence from Conversion from Hexadecimal to Binary, the result follows by concatenating these strings:

$6 \mathrm C 5_H = 110 \, 1100 \, 0101_2$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $16$