Octal to Hex

You will probably not run into many occasions that call for the conversion of octal numbers to hex. Should the need arise, conversion is a two-step procedure. Convert the octal number to binary; then convert the binary number to hex. The steps to convert 53.7₈ to hex are shown below:

Regroup the binary digits into groups of four and add zeros where needed to complete groups; then convert the binary to hex.

Solution: 53.7₈ equals 2B.E₁₆

Convert the following numbers to hex:

Q.83 74₈.
Q.84 512₈.
Q.85 0.03₈.
Q.86 14.42₈.

HEX CONVERSION

The procedures for converting hex numbers to binary and octal are the reverse of the binary and octal conversions to hex.

Hex to Binary

To convert a hex number to binary, set up the number in the block format you used in earlier conversions. Below each hex digit, write the four-digit binary equivalent. Observe the following example:

Convert ABC₁₆ to binary:

Solution: ABC₁₆ = 101010111100₂

Hex to Octal

Just like the conversion of octal to hex, conversion of hex to octal is a two-step procedure. First, convert the hex number to binary; and second, convert the binary number to octal. Let's use the same example we used above in the hex to binary conversion and convert it to octal:

Convert these base 16 numbers to their equivalent base 2 and base 8 numbers:

Q.87 23₁₆.
Q.88 1B₁₆.
Q.89 0.E4₁₆.
Q.90 45.A₁₆.