● Conversion from a binary number to an octal number or hexadecimal number
The following properties are used to convert a binary number to an octal
number or hexadecimal number.
• Three binary number digits can be expressed as one octal number
digit.
• Four binary number digits can be expressed as one hexadecimal
number digit.
Example
Converting (11010)2 to an octal number and hexadecimal number
Conversion from a binary number to
an octal number
Separate the value by groups of three
digits starting from the final digits
11
010
3
2
Conversion from a binary number to a
hexadecimal number
Separate the value by groups of four
digits starting from the final digits
Convert each group of
digits into decimal
numbers
1
1010
1
10
(32)8
(1A)16
●Conversion from an octal number or hexadecimal number to a
binary number
To convert an octal number or hexadecimal number to a binary number,
convert each octal number digit into three binary number digits, and each
hexadecimal number digit into four binary digits.
Example
Converting (43)8 and (F5)16 to binary numbers
Conversion from an octal number to a
binary number
4
100
100
3
Conversion from a hexadecimal
number to a binary number
F
Convert each digit
11
into binary numbers
011(Add a third digit)
(100011)2
1111
1111
5
101
0101(Add a fourth digit)
(11110101)2
Radix conversion overview
Divide the value of the decimal number by 2 repeatedly to determine
the quotients and remainders. Continue until the final quotient equals
“1.” Arrange the final quotient of “1” and each remainder in reverse
order to convert the resulting figures to a binary number.
Separate the binary number into groups of three digits starting from
the final digits. Multiply each digit by 2 0 , 2 1 , or 2 2 , and add the
resulting values to convert the figures into an octal number. Or
similarly, separate the binary number into groups of four digits.
Multiply each digit by 20, 21, 22, or 23, and add the resulting values
to convert the figures into a hexadecimal number.
Decimal
number
Binary
number
Octal
number
Hexadecimal
number
(30)10
(11110)2
(11 110)2
(1 1110)2
(3 6)8
From the last digit of the binary number, multiply each successive
digit by its corresponding factor (20, 21, 22, etc.). Add the resulting
values to convert the figures into a decimal number.
(1 E)16
Divide each digit of the octal number or hexadecimal number by 2
to determine the quotients and remainders. Continue until the final
quotient equals “1.” Arrange the final quotient of “1” and each
remainder in reverse order. Combine the resulting values starting
with those corresponding to the first digits of the original number, to
convert the figures to a binary number.
* When converting to a binary number, if each digit of the original number does
not equate to three or four digits, add a “0” before the resulting value until it
contains the required amount (three digits for an octal number, four digits for
a hexadecimal number).
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