Conversion from a Binary to Octal and Vice Versa
Binary to octal
To convert from binary to octal, we start from the LSB and then group three digits at
a time and replace them by the decimal equivalent as follow:
Ex) Convert (101101010)
2
into an equivalent octal number.
Ex) Convert (1011110)
2
into an equivalent octal number.
Ex) Convert (1101.0111)
2
into an equivalent octal number.
In this case, we complete the real part by adding two 0s (left padding) and adding two
0s on the right side (right padding).
Ex) Convert (11010111.0101)
2
into an equivalent octal number.
Octal to binary
To convert from octal to binary, each octal digit is converted into a 3-bit-equivalent
binary number.
Ex) Convert (235)
8
into an equivalent binary number.
Ex) Convert (47.321)
8
into an equivalent binary number.
Conversion from a Binary to Hexadecimal and Vice Versa
Binary to hexadecimal
To convert from binary to hexadecimal, we start from the LSB and then group four
digits at a time and replace them by the decimal equivalent as follow:
Ex) Convert (110011110)
2
into an equivalent hexadecimal number.
Ex) Convert (111011.011)
2
into an equivalent hexadecimal number.
Ex) Convert (1010101011.011010)
2
into an equivalent hexadecimal number.
Hexadecimal to binary
To convert from hexadecimal to binary, each hexadecimal digit is converted into a 4-
bit equivalent binary number.
Ex) Convert (29C)
16
into an equivalent binary number.
Ex) Convert (9E.AF2)
16
into an equivalent binary number.
Conversion from Octal to Hexadecimal and Vice Versa
Octal to hexadecimal
To convert from octal to hexadecimal, the following steps are followed:
(i) First convert the octal number to its binary equivalent.
(ii) Then form groups of 4 bits, starting from the LSB.
(iii) Then write the equivalent hexadecimal number for each group of 4 bits.
Ex) Convert (247)
8
into an equivalent hexadecimal number.
Ex) Convert (36.532)
8
into an equivalent hexadecimal number.
Ex) Convert (735.461)
8
into an equivalent hexadecimal number.
Hexadecimal to octal
Similarly, to convert from hexadecimal number into an octal number:
(i) First convert the hexadecimal number to its binary equivalent.
(ii) Then form groups of 3 bits, starting from the LSB.
(iii) Then write the equivalent octal number for each group of 3 bits.
Ex) Convert the following hexadecimal numbers into equivalent octal numbers.
(a) A72E (b) 4.BF85
(b)