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 = 1012 (by adding 4 +0+1) read as one zero one
810 = 10002 (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.
8⁴ 8³ 8² 8¹ 8⁰ 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 = 7₈
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.
5⁴ 5³ 5² 5¹ 5⁰ INDEX
625 125 25 5 1 BASE 10
BASE 5
Converting numbers from Base 10 to Base 5 and visa versa.
a) 20₅ = 40₁₀ (4x5 + 0x1)
b) 78₅ = 303₁₀ (3x25 + 0x5 + 3x1)
c) 246₅ = 1441₁₀ (1x125 + 4x25 + 4x5 + 1x1)
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