**1.1 BASE 2**

**Concept**: It is easy to understand the concept by looking at this table.

2

^{8}2

^{7}2

^{6}2

^{5}2

^{4}2

^{3}2

^{2}2

^{1}2

^{0}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. 3

_{10}= 11

_{2}(by adding 2 + 1)

**read as one, one.**

5

_{10}= 101

_{2 (by adding 4 +0+1) read as one zero one}

_{ 8}

_{10 }

_{ = 1000}

_{2 (by adding 8+0+0+0) read as one zero zero zero}

_{ 13}

_{10}

_{ = 1101}

_{2}

_{ (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. 111}

_{2}

_{ = 7}

_{10}

_{ (4+2+1)}

_{ 10101}

_{2}

_{ = 21}

_{10}

_{ (16+0+4+0+1)}

_{ 111001}

_{2}

_{ = 57}

_{10}

_{ (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}⁴

_{ 8}³

_{ 8}²

_{ 8}¹

_{ 8}⁰

_{ 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) 7}₁₀

_{ = 7}₈

b) 8₁₀ = 10₈ (1x8 + 0x1)

c) 14₁₀ = 16₈ (1x8 + 6x1)

d) 45₁₀ = 55₈ (5x8 + 5x1)

e) 249₁₀ = 371₈ (3x64 + 7x8 + 1x1)

Similarly:

f) 15₈ = 13₁₀ (8 + 5)

g) 134₈ = 92₁₀ (64 + 24 + 4)

_{}_{ 1.3 BASE 5}

_{Base 5 uses digits 0,1,2,3,4 only.}

_{ }

_{ 5}⁴

_{ 5}³

_{ 5}²

_{ 5}¹

_{ 5}⁰

_{ INDEX}

_{ 625 125 25 5 1 BASE 10}

_{ BASE 5}

_{Converting numbers from Base 10 to Base 5 and visa versa.}

_{a) 20}₅

_{ = 40}₁₀

_{ (4x5 + 0x1)}

_{b) 78}₅

_{ = 303}₁₀

_{ (3x25 + 0x5 + 3x1)}

_{c) 246}₅

_{ = 1441}₁₀

_{ (1x125 + 4x25 + 4x5 + 1x1) }

_{p/s}

_{I think you should understand the whole concept by now.}

_{Any problems, just leave your comments..... }

_{ }

_{ }

## 10 comments:

I don't understand :'(

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...

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

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

i dont undertand how you add it ;(

i mean the base 10 to 2

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.

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

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

TQ.

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

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