Converting between Bases

Fun fact: Converting between bases of powers of $2$ is even easier!

• To convert a number from base $2$ to base $16$, group every 4 bits together, and simply convert them to the respective hexadecimal symbol. Here is a shorthand table with all possible 4-bit configurations:

  $N_{16}$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$\mathrm A$	$\mathrm B$	$\mathrm C$	$\mathrm D$	$\mathrm E$	$\mathrm F$
  $N_2$	$0000$	$0001$	$0010$	$0011$	$0100$	$0101$	$0110$	$0111$	$1000$	$1001$	$1010$	$1011$	$1100$	$1101$	$1110$	$1111$

  Example: $011111000010_2 = $$0111$$1100$$0010$$_2$ = $7$$\mathrm C$$2$$_{16} = 7\mathrm C2_{16}$.

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• Similarly, to convert from base $2$ to base $8$, group every 3 bits together and convert them to an octal digit:

  $N_{8}$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
  $N_2$	$000$	$001$	$010$	$011$	$100$	$101$	$110$	$111$

  Example: $011111000010_2 = $$011$$111$$000$$010$$_2$ = $3$$7$$0$$2$$_{8} = 3702_8$.