Are there any facts about binary code?

Answer 1

That depends on what you regard as interesting, but there are certainly facts.

Just as moving decimal digits to the left or right raises or lowers the value by a power of 10 (shifting the digits 12 one position to the left becomes 120, which is 10 x 12), shifting binary digits (bits) left or right raises or lowers the value by a power of 2. This fact is true in any base, where the shift raises or lowers by a power of the base. In digital computing, however, this fact makes it possible to raise and lower values by a power of 2 extremely quickly. That is, to double a value, shift all the bits one position to the left. To quadruple a value, shift two places to the left, and so on.

Base-2 is directly related to base-4, base-8, base-16, base-32 and so on. What this means is that we can directly translate any binary number into any base that is an exact power of 2. This makes it possible to notate long sequences of binary digits using much shorter sequences in a higher base. For instance, if we split up a long sequence of bits into pairs of bits, we find there are only 4 combinations for each pair (00, 01, 10 and 11), each of which can be denoted using a single base-4 digit (0, 1, 2 and 3). Thus we can denote a 32-bit sequence using just 16 base-4 digits. By the same token, base-8 (octal) is useful for denoting groups of 3 bits, thus a 24-bit binary number can be reduced to an 8 digit octal value. Base-16 (hexadecimal) digits allows us to represent groups of 4 bits, while base-32 uses groups of 5 bits, and so on. However, we typically use hexadecimal for binary notation because 4 bits is half a byte (a nybble) and two hex digits therefore represents one full byte (8 bits). Thus the 8-bit binary value 10101100 can be split into two nybbles, 1010 and 1100, each of which can be represent by one hexadecimal digit. 1010 binary is 10 decimal, which is A in hexadecimal (the letters A to F represent decimal digits 10 to 15), while 1100 binary is 12 decimal which is C in hexadecimal. Thus AC16 is the hexadecimal representation of the binary value 10101100. This is more commonly written as 0xAC, or ACh. An 8 digit hexadecimal value such as 0xAC15FF01 make it possible to denote 32-bit binary values very easily. And converting back to binary is simply a matter of translating each hexadecimal digit back to its 4-bit binary equivalent. Thus A becomes 1010.

The mechanics of physically storing digital data might be regarded as interesting. They're certainly factual. Although we use the digits 1 and 0 to represent binary values, computers do not. However, binary values can be denoted using any two symbols, whether real or conceptual; apples and Pears, chalk and cheese, black and white, true or false. So long as the computer can differentiate between any two states it can differentiate digits and therefore store numbers. In computer memory, a 1 is represented by a capacitor with sufficient charge while a 0 is represented by a capacitor with insufficient charge. The charge is filled or drained via a transistor, and each pair of capacitor and transistor forms a single cell in memory, each capable of storing exactly 1 bit of information. Capacitors are like leaky cups while transistors are like taps that can either refill the cup or allow it to drain. Because a charge drains away very quickly, the transistors must constantly refill the capacitors to maintain their state, hence memory must be refreshed many times a second. Thus when all power is lost, the contents of memory are lost. However, memory is a bit like our short term memory. It's extremely fast but is highly volatile.

Thus computers use data storage devices such as hard disk in order to hold data more permanently, the equivalent of our long-term memory. It's slower, but does not require power to maintain its state. Hard-disks use magnetic medium to store digital information, using sequences of positively and negatively charged particles. However, it is not the polarity of the particles that denotes the value of a bit, it is the flux transitions from one state to the other that denotes a 1, while the lack of a transition denotes a 0. However, in order to mark where one bit ends and the next begins, there is also regular alternating flux transition interleaved into the actual data. This regulatory flux transition ensures there is always at least one flux transition for every two bits of actual data. Without this, long sequences of 0 bits would be impossible to differentiate, regardless of how accurately the speed of the medium is controlled.

Other methods of storing binary data include the original punch-cards, where the presence of a hole denotes a 1 while the absence of a hole denotes a 0. Unlike hard-drives, punch cards are read very slowly by comparison, but at a highly regular rate, thus they do not require transitions for timing. Passing the cards through a reader at a regular rate (using sprocketed drives) allows the computer to update its internal memory accordingly. Optical drives such as CD, DVD and BluRay use a series of pits and lands (or flats) similar to punch cards, but due to the high speed and lack of accuracy, they also require timing transitions the same as hard-drives. The point is that regardless of the method used to store data, the mechanics of differentiating between any two states remains largely the same -- there are no digits as such, only physical properties that can be translated into digits that we humans can easily understand.