**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

__Hexadecimal (b = 16)__

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

Hopefully you find this helpful.

P.S. I hope the next
update to the TI-84 Plus CE and the Casio fx-CG 50 have adds operating system base
conversions and Boolean functions. HP Prime has base conversions.

I have am working on a retro review, working on blog about
adjustable rate mortgages, and HHC 2018 is coming up at the end of the month (http://hhuc.us/2018/).

Eddie

All original
content copyright, © 2011-2018. Edward
Shore. Unauthorized use and/or
unauthorized distribution for commercial purposes without express and written
permission from the author is strictly prohibited. This blog entry may be distributed for
noncommercial purposes, provided that full credit is given to the author. Please contact the author if you have
questions.

## No comments:

## Post a Comment