Hex–Binary and Binary–Hex Conversions

        A hexadecimal number can be converted into its binary equivalent by replacing each hex digit with its
four-bit binary equivalent. We take the four-bit equivalent because the base of the hexadecimal number
system is 16 and it is the fourth power of the base of the binary number system. All we have then to
remember is the four-bit binary equivalents of the basic digits of the hexadecimal number system. A
given binary number can be converted into an equivalent hexadecimal number by splitting the integer
and fractional parts into groups of four bits, starting from the binary point on both sides. The 0s can
be added to complete the outside groups if needed.
Example 1.7
Let us find the binary equivalent of (17E.F6)16 and the hex equivalent of (1011001110.011011101)2.
Solution
• The given hex number = (17E.F6)16
• The binary equivalent = (0001 0111 1110.1111 0110)2
= (000101111110.11110110)2
= (101111110.1111011)2
• The 0s on the extreme left of the integer part and on the extreme right of the fractional part have
been omitted.
• The given binary number = (1011001110.011011101)2
= (10 1100 1110.0110 1110 1)2
• The hex equivalent = (0010 1100 1110.0110 1110 1000)2
= (2CE.6E8)16