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# Floating Point Base Conversions with Scientific Calculators

Floating Point Base Conversions with Scientific Calculators
Introduction
Any scientific calculator that has base conversions will operate on integers only.  But what if we want to find hexadecimal representation of π?  According to the TI LCD Programming there is a procedure.
This blog post will focus on conversions between binary (base 2), octal (base 8), hexadecimal (base 16), and decimal (base 10).  This can easily be worked with other bases.
Decimal to Other Bases
Let x = the number to be converted.
Steps:
1. Let n be the number of decimal places x has.  Designate b to the designated base.  Here’s a point:  please be aware of your decimal point.  Being aware of your values is key coming up with the correct conversion.
2. In Decimal mode, Multiply x * b^(n-1).
3. Convert the result to the destination base. The conversion will be shown as a decimal.  You will need to place the decimal point in the answer yourself.
Example:  Convert 3.1415 to Binary, Octal, and Hexadecimal.
x = 3.1415 has 4 decimal places, hence n = 4.
Binary   (b = 2)
In Decimal mode:  3.1415 * 2^(4- 1) = 25.132
Convert to Binary ([2nd/SHIFT] (BIN)), display:  11001
Since 3_10 = 11_2, place the decimal point as such:  11.001
Octal  (b = 8)
In Decimal mode:  3.1415 * 8^(4- 1) = 1608.448
Convert to Octal ([2nd/SHIFT] (OCT)), display:  3110
Since 3_10 = 3_8, place the decimal point as such:  3.110
In Decimal mode:  3.1415 *16^(4- 1) = 12867.584
Convert to Octal ([2nd/SHIFT] (HEX)), display:  3243
Since 3_10 = 3_16, place the decimal point as such:  3.243
As a result:  3.1415_10 ≈ 11.001_2 ≈ 3.110_8 ≈ 3.243_16

Other Bases to Decimal
Let x = the number to be converted.
Steps:
1. Let n be the number of decimal places x has.  Designate b to the designated base.  Here’s a point:  please be aware of your decimal point.  Being aware of your values is key coming up with the correct conversion.
2. In the destination base mode, type the number without the decimal point.
3. Convert the number to decimal. (Change the number to Decimal mode)
4. Divide the result by b^n.
Examples
Example 1:  Convert 11.01101_2 to decimal.
1.01101_2 has 5 decimal places, n = 5. Enter in BIN mode:  1101101.  Remember not to include decimal point.
Convert to decimal ([2nd/Shift] (DEC)):  109
To get the final result:  109 / 2^5 = 3.40625
Example 2:  Convert 4.7076_8 to decimal.
4.7076_8 has 4 decimal places, n = 4. Enter in OCT mode:  47076.  Remember not to include decimal point.
Convert to decimal ([2nd/Shift] (DEC)):  20030
To get the final result:  20030 / 8^4 = 4.890136719
Example 3:  Convert  3A.19B1_16 to decimal
3A.19B1_16 has 4 decimal places, n = 4. Enter in HEX mode:  3A19B1.  Remember not to include decimal point.
Convert to decimal ([2nd/Shift] (DEC)):  3807665
To get the final result:  3807665 / 16^4 = 58.10035706
Source:
Texas Instruments TI LCD Programmer User Manual.  Texas Instruments. 1981.
You can find a PDF of the manual from Datamath’s website here:  http://www.datamath.org/Sci/Slanted/LCD-Programmer.htm