Yesterday, Alfred Thompson asked "Why is it important for CS students to understand binary?" on Twitter which led to a number of interesting responses. Alfred summarized and wrote his own thoughts on his blog.

I wanted to add a comment but I already wrote a post for yesterday so put it off until today.

First let me say that you can have a very successful career in tech and not really know binary or number bases other than 10. That career could be as as programmer, software engineer, network specialist, devops or in many other areas that fall on the CS side of tech.

You also can't really get through a CS program without learning about binary. If you're self taught or go to a code school then that's another story.

The question is, is it worth the time spent.

One can easily argue that systems - that is low level, close to the metal knowledge is one of the two "latins" of CS, the other being CS theory. You might not explicitly use either but they give you a stronger foundation in everything. You also can't study systems without a good knowledge of binary so if you want to do anything low level, you need it.

What about beyond those easy but not all to convincing to new students answers?

Let's loo at a few things we can do with binary.

A big part of binary notation is that you can look at data as a string of bits. You can also manipulate that data using things like and , or , not , and xor .

At it's core and let's you turn off bits. And any bit with a 0 and it will become a 0. And it with a 1 and it stays the same.

\begin{array}{ccccc} &1 & 1 & 0 & 0\\ and &0 & 1 & 0 & 1\\\hline &0 & 1 & 0 & 0\\ \end{array}

Or is used to turn on bits. You or any bit with a 1 and it gets turned on. Or it with a 0 and it stays as it was. $$ \begin{array}{ccccc} &1 & 1 & 0 & 0\\ or &0 & 1 & 0 & 1\\\hline &1 & 1 & 0 & 1\\ \end{array} $$ Xor a bit with a 1 and the bit flips, with a 0 it stays the same. $$ \begin{array}{ccccc} &1 & 1 & 0 & 0\\ xor &0 & 1 & 0 & 1\\\hline &1 & 0 & 0 & 1\\ \end{array} $$

What can we do with this? For one thing, image processing. Students frequently play with images where each pixel is represented as a 24 bit color. Three bytes, one each for red, green, and blue. Each byte is really 8 bits. We can use bitwise operations on the binary digits to turn on or off color.

Let's say we have this rgb triple: (200, 15, 80) which in hexadecimal is C8 0F 50 or 10111000 00001111 01010000 in binary. If we want to turn off the reddest reds we could and the color with 00001111 11111111 11111111 or 0FFFFF:

$$ \begin{array}{cccc} & 10111000 & 00001111 & 01010000\\ and & 00001111 & 11111111 & 11111111\\\hline & 00001000 & 00001111 & 01010000\\ \end{array} $$ Yes, you could just use the base 10 values and keep on calling color setting and conversion functions but if you understand binary it's quicker and easier and what's going on will actually make sense.

Of course you probably wouldn't write out the binary but would rather use the hex notation which once a student realizes is just 4 bit groupings of binary becomes really easy. As a bonus, once you're used to binary and hex those hexadecimal color values will all of a sudden make sense.

This is just the tip of the image processing and graphics iceberg with respect to binary.

Related although I haven't played with it myself, I'd imagine you could use these types of bitwise operations on images to play with steganography.

Another use of binary is in cybersecurity. Things like buffer overflows and blowing the stack all make much more sense if you know how memory is arranged and that's easier to understand if you understand binary, bytes, and word sizes. I do experiments with my classes when we use C or C++ where they access arrays off the ends and end up messing with neighboring variables. It seems like magic unless you know about memory and to know memory you need to know binary.

How about image file formats? Many image file formats start with a fixed size header. Here's the header definition for the GIF file format:

Offset Length Contents 0 3 bytes "GIF" 3 3 bytes "87a" or "89a" 6 2 bytes <Logical Screen Width> 8 2 bytes <Logical Screen Height> 10 1 byte bit0: Global Color Table Flag (GCTF) bit 1..3: Color Resolution bit 4: Sort Flag to Global Color Table bit 5..7: Size of Global Color Table:2^(1+n) 11 1 byte <Background Color Index> 12 1 byte <Pixel Aspect Ratio> 13 ? bytes <Global Color Table(0..255 x 3 bytes) ? bytes <Blocks> 1 bytes <Trailer> (0x3b)

The header info is defined bit by bit so you have to know about binary and know how to manipulate data on a bit level.

Those were three biggies but there are other places where knowing binary makes tons of sense:

flag type parameters

understanding floating point numbers

using shifts for quick doubling and halving of data

Does this mean that binary has to be or should be in a first course? No. Should it be somewhere? Certainly and rather than doing binary because it's on the test or because "you should know it" you can pick and choose your spots and cover it when it will be fun and interesting for your kids.

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