2.2
Natural Numbers
41
To convert from binary to octal, you start at the rightmost binary digit
and mark the digits in groups of threes. Then you convert each group of
three to its octal value.
111
101
100
754
Let’s convert the binary number 1010110 to octal, and then convert that
octal value to decimal. The answer should be the equivalent of 1010110 in
decimal, or 86.
1
010
110
12 6
1*8
2
=1*6
4=6
4
+2*8
1
=2* 8
±=1
6
+6*8
0
=6* 1=
6
86
The reason that binary can be immediately converted to octal and octal to
binary is that 8 is a power of 2. There is a similar relationship between
binary and hexadecimal. Every hexadecimal digit can be represented in
four binary digits. Let’s take the binary number 1010110 and convert it to
hexadecimal by marking of the digits from right to left in groups of four.
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 Fall '10
 MARIANAKANT
 Binary numeral system, Decimal, octal value, rightmost binary digit

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