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Fourth, Fifth, and Sixth Passes Through Step 4

Nov 26,2008 by alperen

image

Fourth, Fifth, and Sixth Passes Through Step 4

Decimal Number to Be Converted

235

           

Remainder (from previous step/column)


107

43

11

11

3

3

Next lower 2x value as compared to previous step


64

32

16

8

4

2

Binary number

1

1

1

0

1

0

1

Remainder

107

43

11

11

3

3

1


With a power of 2 of 23, another binary 1 was added to the binary number. For 22 (4), 4 is larger than the remainder of 3, so a binary digit of 0 was added to the number. Finally, in the third of the 3 bold columns, for 21 (2), 2 is less than the remainder of 3, causing a binary digit of 1 to be added, with the remainder being recalculated as 1.

The final pass through Step 4 is shown in Table B-11. The logic is not any different from the other passes through Step 4, other than the fact that you should know that this is the last time to use Step 4 because the next lower power of 2, 20 (1), is the last possible digit in a binary number.


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» Converting from Decimal to Binary
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» First Pass Through Step 4 of the Conversion Algorithm, with 26 (64) as the Power of 2
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» Second Pass Through Step 4, for 25 (32)
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» Final Pass Through Step 4 of Decimal-to-Binary Conversion of Decimal 100
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» Last Pass Through Step 4, for 20 (1)
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