(2)Radix conversion
“Radix conversion” deals with the replacement of one number system
with another.
The method of radix conversion is summarized below.
(
1
3
= 2 ×1
= 8 ×1
=
8
0
2
+ 2 ×0
+ 4 ×0
+
0
1
1
+ 2 ×1
+ 2 ×1
+
2
0
)2
0
+ 2 ×0
+ 1 ×0
+
0
= (10) 10
●Conversion from a decimal number to a binary number
By repeatedly dividing a decimal number by 2, it can be easily converted
into a binary number.
Example Converting (10)10 to a binary number
2
10 …0
2
5
…1
2
…0
2
1
Reference
Reading and writing binary
numbers
If “1010” is written as is, it would not be
possible to differentiate a binary number
from a decimal number. To be represented as a binary number, the value
must be bracketed using parentheses
and denoted with a “2” after it. The resulting notation would then be “(1010)2.”
This number can be read digit by digit
as “One. Zero. One. Zero.”
Reference
0
n
← Write the remainder.
Regardless of which value n represents,
“n0 = 1” (the zero power equals “1”) by
definition.
← Divide by 2 until the quotient equals “1.”
Decimal Number Composition
Reference
In the same sequence as shown by the arrow, write
the final quotient and each remainder starting from
the beginning of the new value, to convert the
decimal number to a binary number.
(10)10 → (1010)2
A “radix” shows how many different
numbers can be expressed within one
digit.
For example, a binary number is composed using the two numbers “0” and
“1,” therefore its radix is “2.”
Basic theory
Example Converting (1010)2 to a decimal number
Radix
Chapter 7
●Conversion from a binary number to a decimal number
In the same way that each digit in a decimal number system represents
“100”, “101”, “102”, and so on, the digits in a binary number system signify
“20”, “21”, and “22”, etc. Using these properties, a binary number can be
converted to a decimal number.
Reference
(1
3
2
3 )10
0
2
1
0
= 10 ×1 +10 ×2 +10 ×0 +10 ×3
= 1000×1 + 100×2 + 10×0 + 1×3
= 1000 + 200 + 0 + 3
= 1203
158