LESSON
03 – CONVERSIONS FROM BASE 10
LESSON NOTE
FROM BASE 10 TO BASE
2
OPTION
#1 – SUBTRACTION APPROACH
In this
approach, we check if our number is larger than a power of two. We start with 128, then 64, then 32, … If the number is greater than the number it
is checked against, our next digit is 1, otherwise, it is 0.
STEP #1
if number
greater than or equal to 128
Leftmost digit is 1
number = number - 128
else
Leftmost digit is 0
end if
STEP #2
if number
greater than or equal to 64
Next digit is 1
number = number - 64
else
Next digit is 0
end if
STEP #3
if number
greater than or equal to 32
Next digit is 1
number = number - 32
else
Next digit is 0
end if
STEP #4
if number
greater than or equal to 16
Next digit is 1
number = number - 16
else
Next digit is 0
end if
STEP #5
if number
greater than or equal to 8
Next digit is 1
number = number - 8
else
Next digit is 0
end if
STEP #6
if number
greater than or equal to 4
Next digit is 1
number = number - 4
else
Next digit is 0
end if
STEP #7
if number
greater than or equal to 2
Next digit is 1
number = number - 2
else
Next digit is 0
end if
STEP #8
if number
is equal to 1
Rightmost digit is 1
number = number - 1
else
Rightmost digit is 0
end if
OPTION #2
– REMAINDER APPROACH
We simply
continuously divide our number by two.
The remainder (0 or 1) is a digit in our binary number. An example is the best way to understand
(and explain) the method.
Example –
Convert 157 to binary.
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157 ÷ 2 = 78
78 ÷ 2 = 39
39 ÷ 2 = 19
19 ÷ 2 = 9
9 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
1 ÷ 2 = 0
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with a
remainder of 1
with a remainder of 0
with a remainder of 1
with a remainder of 1
with a remainder of 1
with a remainder of 0
with a remainder of 0
with a remainder of 1
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(the
bottom is the leftmost number)
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Therefore
10011101 is our answer. This approach
may not give you 8 digits. You may be
forced to tack on zeros at the beginning.
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