10
Digital Electronics
• Any 0s on the extreme left of the integer part and extreme right of the fractional part of the equivalent
binary number should be omitted. Therefore, (011111100.010110) 2 = (11111100.01011) 2
• The given binary number = (1110100.0100111) 2
• (1110100.0100111) 2 = (1 110 100.010 011 1) 2
= (001 110 100.010 011 100) 2 = (164.234) 8
1.14 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
1.15 Hex–Octal and Octal–Hex Conversions
For hexadecimal–octal conversion, the given hex number is firstly converted into its binary equivalent
which is further converted into its octal equivalent. An alternative approach is firstly to convert the
given hexadecimal number into its decimal equivalent and then convert the decimal number into an
equivalent octal number. The former method is definitely more convenient and straightforward. For
octal–hexadecimal conversion, the octal number may first be converted into an equivalent binary
number and then the binary number transformed into its hex equivalent. The other option is firstly to
convert the given octal number into its decimal equivalent and then convert the decimal number into
its hex equivalent. The former approach is definitely the preferred one. Two types of conversion are
illustrated in the following example.
Example 1.8
Let us find the octal equivalent of (2F.C4) 16 and the hex equivalent of (762.013) 8
Digital Electronics
• Any 0s on the extreme left of the integer part and extreme right of the fractional part of the equivalent
binary number should be omitted. Therefore, (011111100.010110) 2 = (11111100.01011) 2
• The given binary number = (1110100.0100111) 2
• (1110100.0100111) 2 = (1 110 100.010 011 1) 2
= (001 110 100.010 011 100) 2 = (164.234) 8
1.14 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
1.15 Hex–Octal and Octal–Hex Conversions
For hexadecimal–octal conversion, the given hex number is firstly converted into its binary equivalent
which is further converted into its octal equivalent. An alternative approach is firstly to convert the
given hexadecimal number into its decimal equivalent and then convert the decimal number into an
equivalent octal number. The former method is definitely more convenient and straightforward. For
octal–hexadecimal conversion, the octal number may first be converted into an equivalent binary
number and then the binary number transformed into its hex equivalent. The other option is firstly to
convert the given octal number into its decimal equivalent and then convert the decimal number into
its hex equivalent. The former approach is definitely the preferred one. Two types of conversion are
illustrated in the following example.
Example 1.8
Let us find the octal equivalent of (2F.C4) 16 and the hex equivalent of (762.013) 8