Anyone know how to convert hexadecmial numbers to octal expansion?

Question

I've been sitting here trying to figure this out for over an hour.

The question says: convert the hexadecimal number ABB093BABBA to its octal expansion.

I've tried every which way that I know how, but I keep getting answers with scientific notation. Please help me someone.

Answer 1

If you're doing it by hand, the easiest way I know is to use binary (base-2) as an intermediate.

It turns out that it's very easy to convert between base 16 (hex) and base 2; and between base 8 (octal) and base 2. This has to do with the fact that 16 is a power of 2; and 8 is also a power of 2 (but never mind that now).

Step 1: To convert from hex to binary, just convert each individual hex digit into exactly four binary digits:
0 -> 0000
1 -> 0001
(etc.)
E -> 1110
F -> 1111

So, ABB093BABBA would be:

1010 1011 1011 0000 ...(aw, you do the rest).

Step 2. Every group of THREE binary digits converts directly into one OCTAL digit. So take the long string of 1's and 0's you just wrote, and break them into groups of THREE bits (starting at the RIGHT). To get you started: the end of your bit string will look like this:

...1010 1011 1011 1010 (corresponds to "...ABBA")

Smash together:

...1010101110111010

Break into groups of three:

...1 010 101 110 111 010

Step 3: Assign an octal digit (0 through 7) to each group of 3 bits. (if the leftmost group only has one or two bits, put "0" or "00" in front of it). Using the example above the last five octal digits would be: "...25672"

Works like magic! (And might actually be useful, if anybody still used octal for anything).

Answer 2

Convert Base 16 To Base 8

Answer 3

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Hi, That's the right way of doing it with an important thing to keep in mind that division or sectioning off the bits start from rightmost bit. Just to explain to you why 3 bits in octal and 4 bits in hexadecimal: As per definition of base - A number system of base or radix “r” is a system that uses r distinct symbols to represent any number. Thus, octal with a base of 8, uses 8 distinct symbols (which can be represented by 3 digits as 8=2^3) and hexadecimal with a base of 16, uses 16 distinct symbols (which can be represented by 4 digits as 16=2^4). So as octal is represented using 3 digits, we section off 3 binary numbers starting from right, and as hexadecimal number is represented using 4 digits, we section off 4 binary numbers starting from right. Hope that helps. Regards Kanika

Answer 4

ABB093BABBA (base 16) =

10(16)^10+11(16)^9+11(16)^8+0(16)^7+9(16)^6+
3(16)^5+11(16)^4+10(16)^3+11(16)^2+11(16)^1+10(16)^0

10(8)^20+11(8)^18+11(8)^16+0(8)^14+9(8)^12+
3(8)^10+11(8)^8+10(8)^6+11(8)^4+11(8)^2+10(8)^0

1(8)^21+2^(8)^20+1(8)^19+3(8)^18+1(8)^17+3(8)^16+
0(8)^15+0(8)^14+1(8)^13+1(8)^12+3(8)^10+
1(8)^9+3(8)^8+1(8)^7+2(8)^6+1(8)^5+3(8)^4+1(8)^3+
3(8)^2+1(8)^1+2(8)^0

121313001131312131312 (base 8)

A possible SHORTCUT for converting to base 16 to base 8:

A,B,B,0,9,3,B,A,B,B,A (base 16)
convert each hex digit to base 10
10,11,11,0,9,3,11,10,11,11,10 (base 10)
convert each base 10 number to base 8
12,13,13,00,11,3,13,12,13,13,12 (base 8)
drop the commas
121313001131312131312 (base 8)

note: Do not drop the zeros; zeros hold place in these positional notation systems

Answer 5

ABB093BABBA
=A + B*16 + B*16^2 + A*16^3 + ... (with A=10, B=11) (read it from right to left in increasing powers of 16)
=X
Find the biggest power of 8 that doesn't exceed X. Say it's P. Then the integer part of X/(8^P) is the first digit (going from left to right). Say it's D. Repeat for X-D*8^P.

Answer 6

try converting the base-16 (hexadecimal) number to decimal, then convert to octal.