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Table Of Contents  The TCP/IP Guide
 9  Networking Fundamentals
      9  Backgrounder: Data Representation and the Mathematics of Computing

Previous Topic/Section
Decimal, Binary, Octal and Hexadecimal Numbers
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Pages in Current Topic/Section
123
4
Next Page
Binary, Octal and Hexadecimal Arithmetic
Next Topic/Section

Decimal, Binary, Octal and Hexadecimal Number Conversion
(Page 4 of 4)

Conversions From Decimal to Binary, Octal and Hexadecimal

Now let’s consider conversions from decimal. These require that you perform the opposite of the calculation above: you divide and subtract instead of multiplying and adding.

Conversion From Decimal to Binary

The easiest of the three conversions from decimal is to binary—since the maximum value of each digit is one, there is no dividing, just subtraction. All you do is the following:

  1. Find the largest power of two that is smaller than the number.

  2. Put a “1” in the digit place for that power of two and subtract that power of two from the decimal number.

  3. Repeat steps #1 and #2 until you are reduced to zero.

This is easier to explain using an example and a table, of course. Let's convert the decimal number 689, as shown in Table 5. Again, read the table starting from the upper left, and going down and then across. We start by noticing that 1024 is not less than or equal to 689, so the “1024s” place gets a 0. In the next place, 512 is less than 689, so we make the “512s” place a 1 and subtract 512 from 689 to leave 177. The calculation continues, eventually showing shows that 689 decimal is 1010110001 binary.


Table 5: Decimal to Binary Number Conversion

Decimal Value Before Considering This Digit Place

689

689

177

177

49

49

17

1

1

1

1

Power of Two

210

29

28

27

26

25

24

23

22

21

20

Value of Digit Place

1024

512

256

128

64

32

16

8

4

2

1

Value of Digit Place Equal To or Less Than Current Decimal Number?

No

Yes

No

Yes

No

Yes

Yes

No

No

No

Yes

Subtraction Step

skip

689- 512 = 177

skip

177- 128 = 49

skip

49-32 = 17

17-16 = 1

skip

skip

skip

1-1 = 0

Binary Digits

0

1

0

1

0

1

1

0

0

0

1


Conversion From Decimal to Octal or Hexadecimal

The process for octal and hexadecimal is almost the same, except you must divide by powers of two instead of just subtracting:

  1. Start with the highest power of 16 (hexadecimal) or 8 (octal) that is smaller than the number.

  2. Divide the decimal number by that power, keeping only the integer part of the result.

  3. Keep the remainder after the division is done, for the next step.

  4. Repeat steps #1 to #3 until you get to the “ones” place, and then put there whatever is left after the higher digits were done.

Table 6 shows the same example as Table 5 but goes from decimal to hexadecimal instead of decimal to binary: 689 in decimal is 0x2B1 hexadecimal.


Table 6: Decimal to Hexadecimal Number Conversion

Decimal Value Before Considering This Digit Place

689

689

177

1

Power of 16

163

162

161

160

Value of Digit Place

4096

256

16

1

Value of Digit Place Smaller Than Current Decimal Number?

No

Yes

No

n/a

Division Step

skip

689/256 = 2.691;
use “2” for this digit.

177/16 = 11.0625;
use “B” for this digit.

n/a

Remainder After Division

skip

177

1

n/a

Hexadecimal Digits

0

2

B

1


Previous Topic/Section
Decimal, Binary, Octal and Hexadecimal Numbers
Previous Page
Pages in Current Topic/Section
123
4
Next Page
Binary, Octal and Hexadecimal Arithmetic
Next Topic/Section

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