(E) Converting from One Base to Another
1. The following steps are used to convert a number from
one base to another base.
(a) convert the number to a number in base 10 by using expended notation.
(b) use repeated
division to convert the number in base 10 to the respective bases.
Example 1:
Convert
(a) 110101_{2} to a number in base 5
(b) 43_{5} to a number in base 2
(c) 313_{8} to a number in base 5
(d) 422_{5} to a number in base 8
(e) 100111_{2} to a number in base 8
(f) 157_{8} to a number in base 2
(f) 157_{8} to a number in base 2
Solution:
(a) 110101_{2}
= 1 × 2^{5} + 1 × 2^{4} + 0 × 2^{3}
+ 1 × 2^{2} + 0 × 2^{1} + 1 × 2^{0}
= 53_{10 }←
(Convert from base 2 to base 10)
(b) 43_{5}
= 4 × 5^{1} + 3 × 5^{0}
= 23_{10}
← (Convert from base 5 to base 10)
(c) 313_{8}
= 3 × 8^{2} + 1 × 8^{1} + 3 × 8^{0}
= 203_{10}
← (Convert from base 8 to base 10)
(d) 422_{5 }
= 4 × 5^{2} + 2 × 5^{1} + 2 × 5^{0}
= 112_{10}
← (Convert from base 5 to base 10)
(e) 100111_{2}
= 1 × 2^{5} + 0 × 2^{4} + 0 × 2^{3}
+ 1 × 2^{2} + 1 × 2^{1} + 1 × 2^{0}
= 39_{10 }←
(Convert from base 2 to base 10)
(f) 157_{8 }
= 1 × 8^{2} + 5 × 8^{1} + 7 × 8^{0}
= 111_{10}
← (Convert from base 8 to base 10)
Calculator Computation
1.
Set
the calculator to the ‘BASE’ mode by pressing:
[MODE]
[MODE] [3 (BASE)]
2.
Set
the calculator to the desired number system by pressing:
[BIN]
→ for base 2
[DEC]
→ for base 10
[OCT]
→ for base 8
Key in the following [For (e) and (f) only]:
(e)
[
BIN ] 100111 [ = ] [ OCT ]
The
screen display is: [47_{8}]
Therefore 100111_{2} = 47_{8}
(f)
[
OCT ] 157 [ = ] [ BIN ]
The
screen display is: [1101111]
Therefore
157_{8} = 1101111_{2}
