1.1 number bases
TRANSCRIPT
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Numbers in Base Two
Number
Place value of numbers in base 2
2^4=16
2^3=8
2^2=4
2^1=2
2^0=1
0 01 12 1 03 1 14 1 0 05 1 0 16 1 1 07 1 1 18 1 0 0 09 1 0 0 110 1 0 1 0
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Numbers in base ei ht
Number
Place value of numbers
in base 88^4=0 6
8^3=12
8^2=6
8^1=8
8^0=1
0 01 1
2 2
456 678 1 0
1 110 1 228 1 2
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Numbers in base Five
Number
Place value of numbers
in base 55^4=62
5^3=12
5^2=2
5^1= 5^0=1
0 01 1
2 23 34 4
5 1 06 1 17 1 28 1 39 1 4
10 2 0
2 1 0 28
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Value of a digit of a
number in base 2,8 and 5Example:
1. 11012 = 1 x 22 = 4
2. 50368 = 5 x 83 =2560
3. 24105= 4 x 52 = 100
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Writing Numbers in Base 2, 8 and 5 i
n
Expanded Notation
Examples:
1. 10112= 1 x 23 + 0 x 22 + 1 x 21 + 1 x 20
2. 3478 = 3 x 82 + 4 x 81 + 7 x 80
3. 1425= 1 x 52 + 4 x 51 + 2 x 50
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1.1d Converting Numbers in
Base Two, Eight and Five toBase 10 and vice Versa
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Steps to Remember:
1. Write the number in expanded notation
2. Simplify the expanded notation into a single number.
Examples:
(i) 10112 = 1 x 23 + 0 x 22 + 1 x21 +1 x 20 =1110
(ii) 2768 = 2 x 82 + 7 x 81 + 6 x 80=19010
(iii) 1345 = 1 x 52 + 3 x 51 + 4 x 50 =4410
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Steps to remember to convert a number in base 10 tonumber in base 2, 8 or 5
(i) Perform repeated division until the quotient is 0.
(ii) Write the number in the new base by referring tothe remainders from bottom to the top.
Example:
(a) Convert 910 to base 22 92 4R 1
2 2R 02 1R 0
0R 1 910 = 10012
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(a) Convert 2810 to base 88 288 3 R4
8 0R 3
2810 = 348
(b) Convert 7610 to base 5
5 765 15R15 3R0
0R3 7610 = 3015
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1112 = 125
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435 = 101112
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1378= 3405
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1378= 3405
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100 111 000 011
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11
1+1 = 210 = 102
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2020
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