Spice Mines of Kessel

If you ever decide to take interest in the computer field, you need to be able to at least read the computer’s native language. Despite what you type on your keyboard, click with your mouse, or read on your screen, the computer doesn’t speak your language. There has to be an interpretation. In fact, the computer’s language is quite a bit simpler than yours.

Computers speak what is called binary. Binary is a numbering system based on two values: 1 and 0. For computers, however, it is a bit (no pun intended) different. Computers can’t even understand 1 or 0. They understand voltage levels. So, think of a 1 representing +5 volts and a 0 as +0.5 volts. So, why not 0 volts for a 0 value? That’s because 0 volts is the same as having no power at all. Without power, that circuit is basically considered off. So, for our mind’s sake, we just stick with 1 and 0. It’s just easier. There’s probably a scientific explanation for it, but that’s beyond the scope of this simple article.

How do we get those 1’s and 0’s arranged into an intelligible order? Well, we must first understand how these things can be grouped. Individually, the 1’s and 0’s are called bits. A group of four bits is called a nibble (or nybble). And a group of eight bits is called a byte. Do you see where I came up with the title of this article?

Each 0 or 1 is a bit
4 bits = 1 nibble (Example: 0110)
8 bits = 1 byte (Example: 00110101)

Typically, we just stick with bits and bytes. I will use bytes for my examples.

Now, we must find out the significance of each bit in a byte. To begin, these bytes are read from right to left (not left to right as English is traditionally read). Think of it as feeding the bits into a feeder and the feeder is on the right. The right-most bit is the first bit to enter into the feeder, and the left-most bit is the last. Therefore, each bit in a byte has a place number ranging from 0 – 7 (from right to left).

Place numbers for bits in a byte.

As you can see from the picture, the right-most bit is in position 0, and the left-most bit is in position 7. Keep in mind that all numberings begin with 0. Now, each position has an assigned value. We will call this value the place value.

The place values of the bits in a byte, like the numbering, begin on the right. The values are: 1, 2, 4, 8, 16, 32, 64, 128. Do you see the pattern? This is called base-2 numbering. All of the values are a power of 2. So, the powers of 2 are: 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7. Do you see the relation with the bit position and it’s power of 2?

The above example with place values and powers of 2.

The power of 2 for each bit in the byte gives its place value. Now that you see the place values and from where that value derived, it’s time to find out what this byte is saying, or the byte’s decimal value. Decimal is the traditional number system that we use. This allows us to convert the binary values to a more easily understood value.

Here is where we must take advice from the Jedi master, Yoda. “You must unlearn what you have learned.” To simplify the process of determining a byte’s decimal value, think of a 1 as yes and a 0 as no. This is the answer to the question, “Do I add this value?” To begin, start with the right-most bit. Ask yourself: “Do I add this value?” How do you know? Well, if this bit is a 1, answer: “Yes.” If it is a 0, answer: “No.”

Let’s begin with the above example. The byte is: 00110101. Begin on the right-most bit. Do I add this value? The bit is a 1, so yes. Now, add it’s value of 1. Our total is: 1. The next bit is a 0, so we don’t add that value. The third bit is a 1, so we add that value, which is 4. Add that to our current total of 1. Our new total is: 1 + 0 + 4 = 5. The fourth bit is a 0. Don’t add its value. The fifth bit is a 1, so add its value of 16. Our new total is: 1 + 0 + 4 + 0 + 16 = 21. The sixth bit is a 1, so add its value of 32. Our new total is: 1 + 0 + 4 + 0 + 16 + 32 = 53. The seventh and eigth bits are both 0, so we don’t add them. Now, look at our final total. The decimal value of this byte is 53.

Once you figure it out, binary is actually quite easy. In fact, you can impress your friends with this nifty binary clock. I personally own one myself. It makes for a good conversation piece. Especially since I’m usually the only one that can read the time with it. Now, you can get the binary clock and be the only one to tell the time.

So, until your fancy new clock arrives at your doorstep, here’s some bytes for you to work on for practice.

• 01010110
• 10010011
• 00001111
• 11001100
• 10000001
• 01101111
• 10101010
• 11101001

Have fun with your binary snack!