The conversion of numbers is common in
mathematics and has been used for many generations. During the creation of computers number
conversion became even more common and necessary. Although once the internet came about and
allowed sharing data the ability to convert these numbers became a bit easier
for the end user. There are many ways of
which you can convert numbers between number bases, and it is fairly simple in
doing so.
Although it may be simple it can seem just a bit
confusing at first. Remember as an adult
you have been using base 10 since you were a child, even though it may not seem
like it. For example, base 10 is simply
numeric values from 0 to 9, but since we do not have a single digit to express
10 like the romans "X" then we add 1 to the tenth place and zero out
the ones place. As another example, when
you are adding 1 to 19, the 1 is technically added to the tenths place and the
ones column is zeroed out.
Now that we have the basic concept of base 10
understood, let's take a look at base-two which is also known as binary. Just as we use base 10 regularly throughout
our lives as mentioned above, base 2 "binary" is very similar. Instead of the highest digit being a 9 and
when a 1 is added it rounds to 10, with binary the highest digit is 0 so when a
1 is added it rounds to one. This is
caused by there being no single digit for two in binary.
With the two first bases described and
understood we can now discuss conversion from base 10 to base 2 (binary) and
back again. Our first base 10 number
being five, base ten converted to binary.
Start off with dividing the desired base such as two into the number we
want to convert. This division will
require we use remainders like we did when we were all in elementary
school. If we take the 2 from base 2 and
divide it into 5 that gives us 2 R 1, then we divide the 2 by 2 again, which
gives us 1 R 0, then we divide the 1 by 2 which gives us 0 R 1. Leaving us with the following remainders
1,0,1. Thus being the binary conversion
of 5 base 10 equals 101 base 2.
Converting base 10 back to binary almost seems a
bit simpler, but it takes a keen eye to understand it. I will use our previous numbers to make it a
bit easier to understand. Our binary
number is 101 base 2 which can be listed as, (1x 22) + (0x21)
+ (1x20) = (1x4) + (0x2) + (1x1) = 4 + 0 + 1 = 5. Now after reviewing this how did I manage to
turn 101 to the equation above? The
digits 101 times two to the place power and add.
When converting a binary number to a decimal has
similar rules that apply. I will use the
previous binary number of 101 that we used above. Now for each number we have a list of power
of two, for example 22 , 21, 20 which is
4,2,1. Take these numbers and plug them
in (4x1)+(2x0)+(1x1) = (4)+(0)+(1) = 5.
This method is simply going backwards from base 10 to binary and binary
back to base 10.
Considering binary is base 2 and hexadecimal is
base 16 and they are both powers of 2 this is a simpler conversion than binary
to decimal. Since hexadecimal numbers
can either be numbers of 0-9 or even characters A-F, you can convert binary
strings to hexadecimals. First off you
need at least a four digit binary number.
We will start with 1010 and add a "small number" to the top
right of each digit a different power of 2, signifying their place as so, 180412
01. This tells you how
many of each number you have, which turns to 8020. Now you can add the four numbers together as
so, 8+0+2+0= 10. All in all the binary
number 1010 would convert to 10 which is an A in the hexadecimal system.
It is extremely important to be able to convert
numbers and truly understand the numeric conversion methods. All information and data is sent and stored
in binary. If an IT professional is
unable to convert numbers as mentioned, then it would be more difficult to
troubleshoot and decode many necessary parts of the IT world. Also, if becoming a system programmer the
ability to easily convert these numbers and translate them in their heads would
allow them to easily understand the system.
This is definitely important if you would like to be able to code in
assembly or machine code.
References
Binary to Decimal Conversion. (n.d.). Retrieved February 5, 2017, from Electronics
Tutorials: http://www.electronics-tutorials.ws/binary/bin_2.html
Bogomolny, A. (n.d.). Implementation of Base
Conversion. Retrieved February 5, 2017, from Cut the Knot:
http://www.cut-the-knot.org/recurrence/conversion.shtml
Englander, I. (2014). The Architecture of Computer
Hardware, Systems Software, & Networking An information technology
approach. Don FowleY.
