Binary

The set of all binary digits is $\{0,1\}$.

The same idea is true for binary numbers, also known as the base-2 system. Imagine we have a number 101010 (base two). We could rewrite it as each digit multiplied by a power of two, like so: $101010_2 = 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0$. If we wanted to get the decimal version of this, we could just simplify: $1 * 2^5 + 1 * 2^3 + 1 * 2^1 = 32 + 8 + 2=42$.

Hexadecimal

The set of all hexadecimal digits is $\{0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F\}$, where A-F have decimal values of 10-15 respectively.

The same idea is true for hexadecimal numbers, also known as the base-16 system. Imagine we have a number 2A (base sixteen). We could rewrite it as each digit multiplied by a power of sixteen, like so: $2A_{16} = 2 * 16^1 + 10 * 16^0$. If we wanted to get the decimal version of this, we could just simplify: $2 * 16^1 + 10 * 16^0 = 32 + 10 = 42$.

Converting decimal to binary or hexadecimal by repeated division

A technique for converting to either binary or hexadecimal is to take the number in decimal and successively divide by either 2 or 16 (depending on the target base), using the remainders to construct the resultant number. Say we want to convert 42 to binary. We would start to divide by 2:

$$ \require{enclose} \begin{array}{rll} 21\\[-3pt] 2 \enclose{longdiv}{42}\kern-.2ex \\[-3pt] \underline{42} \\[-3pt] 0 \\[-3pt] \end{array} $$

Now, we know that the rightmost digit of the resulting binary number is 0, as that is the remainder of the division. We continue by dividing the previous quotient again:

$$ \require{enclose} \begin{array}{rll} 10\\[-3pt] 2 \enclose{longdiv}{21}\kern-.2ex \\[-3pt] \underline{20} \\[-3pt] 1 \\[-3pt] \end{array} $$

The remainder is 1, so the next digit to the left is a 1. Continue dividing until the quotient is 0 (the intermediate three divisions are left as an exercise for the reader):

$$ \require{enclose} \begin{array}{rll} 0\\[-3pt] 2 \enclose{longdiv}{1}\kern-.2ex \\[-3pt] \underline{0} \\[-3pt] 1 \\[-3pt] \end{array} $$

The final remainder is 1, so the leftmost digit of the resulting binary number is 1. Writing all the results next to each other, we get a result of 101010.

The same technique works for converting to hexadecimal (simply divide by 16 repeatedly instead of 2). This technique generalizes to other bases as well.

Other articles

Website Updates

Published: Sun 23 December 2018
By Connor Monahan

In Misc.

tags: website

On merging websites and moving to GitHub pages
read more
Zero Hour Game Jam 2018

Published: Sun 04 November 2018
By Connor Monahan

In Games.

tags: 0hgame

Me and Julia's corn-y submission
read more
Programming various Atmel chips

Published: Sat 11 November 2017
By Connor Monahan

In Hardware.

tags: arduino atmel

Guides for programming several external Atmel chips with an Arduino
read more
Zero Hour Game Jam 2017

Published: Sun 05 November 2017
Updated: Sun 23 December 2018
By Connor Monahan

In Games.

tags: 0hgame

Me and Julia's submission "Satan Cart Horror"
read more
Object Detection with DIGITS and Caffe

Published: Tue 28 February 2017
By Connor Monahan

In Computer Vision.

tags: robotics FRC

This is a simplified version of the notes I took while creating and training a neural network to detect balls in the FRC 2017 game. This will be further updated with additional detail as time allows.

Requirements: Vatic, DIGITS, NvCaffe

An input data set of images with the object for …
read more
Predicting the Presence of Cancer in Medical Images using Convolutional Neural Networks

Published: Wed 15 February 2017
By Connor Monahan

In Research.

Paper submitted to Missouri Junior Science, Engineering, and Humanities Symposium for 2017

Abstract:

Convolutional neural networks model human brain activity from sensory inputs and have been applied to various activities such as driving cars, recognizing speech, and playing complex games. These machine learning algorithms gained popularity in recent years as …
read more
OpenCV Installation Guide
Published: Wed 14 September 2016
By Connor Monahan

In Computer Vision.
- Uncategorized format: link
This guide goes over the installation of OpenCV 3 on Ubuntu.

Install OpenCV 3.0 and Python 2.7+ on Ubuntu

read more
Depth Image Segmentation Using Statistical Methods

Published: Sun 10 January 2016
By Connor Monahan

In Research.

Paper presented to the Junior Science, Engineering, and Humanities Symposium at Maryville University in 2016.

Abstract:

This paper presents an algorithm that utilizes unsupervised machine learning methods for classifying n-objects in a spatial image. Other methods of spatial image segmentation, for example the Laplacian operator and support vector machines (SVM …
read more
Zero Hour Game Jam 2015

Published: Sun 01 November 2015
Updated: Sun 23 December 2018
By Connor Monahan

In Games.

tags: 0hgame

My submission "Radical Harvest Pimps"
read more

Page 1 / 5 »

Other articles

links

social