Sunday, January 3, 2010

FORM 5/Topic 1 - NUMBER BASES

1.1 BASE 2
Concept: It is easy to understand the concept by looking at this table.

     28      27      26     25       24       23    22    21    20    INDEX
  256     128    64     32     16       8     4      2     1     BASE 10
                                                                             BASE 2

Info: Base 10 uses the digits 0,1,2,3,4,5,6,7,8,9.
        Base 2 only uses the digit 0 and 1
How to convert numbers from Base 10 to Base 2?
e.g.  310 = 112 (by adding 2 + 1) read as one, one.
        510 = 101(by adding 4 +0+1) read as one zero one
         810 = 1000(by adding 8+0+0+0) read as one zero zero zero
       1310 = 11012 (by adding 8+4+0+1) read as one one zero one. 

By using the same proses, you can convert numbers from Base 2 to Base 10.

e.g. 1112 = 710  (4+2+1)
       101012 = 2110 (16+0+4+0+1)
       1110012 = 5710 (32+16+8+0+0+1)




1.2  BASE 8
By using the same ideology, we can do the same to numbers in Base 8.


      8        8³         8²        8¹       8     INDEX
  4096     512        64        8         1      BASE 10
                                                            BASE 8


Remember:  Base 8 uses digits 0,1,2,3,4,5,6,7.  There are no digits 8 and 9.

Converting Numbers from Base 10 to Base 8 or from base 8 to Base 10
a)   7₁₀    =  7
b)   8₁₀    =  10  (1x8 + 0x1)

c)  14₁₀   =  16  (1x8 + 6x1)

d)  45₁₀   =  55  (5x8 + 5x1)
e) 249₁₀  =  371  (3x64 + 7x8 + 1x1) 
Similarly:
f)   15     =  13₁₀    (8 + 5)

g)  134    =  92₁₀   (64 + 24 + 4)  

 
1.3  BASE 5
Base 5 uses digits 0,1,2,3,4 only.


    5     5³     5²     5¹     5       INDEX
  625  125    25      5       1      BASE 10
                                               BASE 5

Converting numbers from Base 10 to Base 5 and visa versa.

a)   20    =  40₁₀    (4x5 + 0x1)

b)  78    =  303₁₀   (3x25 + 0x5 + 3x1)

c)  246  =  1441₁₀  (1x125 + 4x25 + 4x5 + 1x1) 

p/s
I think you should understand the whole concept by now.
Any problems, just leave your comments.....

 

10 comments:

Anonymous said...

I don't understand :'(

DESS said...

We have 10 fingers, right?
We count as 1,2,3,4,5,6,7,8,9,10

How do count if we have 8 fingers?
We will count as 1,2,3,4,5,6,7,10.
Right? There will be NO 8 and 9.
Go on counting - 11,12,13,14,15,16,17,20.
21,22,23,24,25,26,27,30.
31,32,33,34,35,36,37,40.
41,42,43,44,45,46,47,50.
51,52,53,54,55,56,57,60.
61,62,63,64,65,66,67,70.
71,72,73,74,75,76,77,100.

The same concept is you have 5 fingers - 1,2,3,4,10,11,12,13,14,20,21,22,23,24,30,31,32,33,34,40,41,42,43,44, 100.

If you have two fingers - it will be faster...
1,10,11,100,101,110,111,1000...

It like that...
Have a nice day...

Anonymous said...

Thank you very much. Help me alot. I was blur when i started with this chapter. but after reading this post. I fully understand. Mind if you send me some questions links? Thank you

DESS said...

Just do the past years SPM paper 1 questions. That's the standard questions (if you are a Malaysian student).

wildness said...

i dont undertand how you add it ;(

wildness said...

i mean the base 10 to 2

DESS said...

Add what? The notes in this post are about converting a number from one base to another. I don't understand what you mean by "how you add it". TQ.

Anonymous said...

Hi Sir,can u help me to solve dis? tq very ,much!!

Given m8 is a two-digit number in base eight. State the higest possible value of m

DESS said...

77 - that's the highest possible 2-digit number in Base 8.
TQ.

Anonymous said...

HOW TO change base 8,5 to number base 10 ??