How do computers store programs and data using binary digits?

Answer 1

They don't! The 1s and 0s are simply how we interpret the data stored inside a computer. There are no numbers as such inside a computer but in order to store data inside a computer we need to speak the same language as the computer. The only language the computer knows is machine code, which is a binary encoded language, thus the easiest way for humans to notate these binary codes is with the digits 0 and 1. In other words, the 0s and 1s are purely a notational convenience.

Binary codes can be represented using any two distinct symbols. Yes and no, true and false, black and white, or positive and negative are all equally valid representations however these concepts are far too abstract for a computer to understand. We need something more basic, something physical that can be easily represented by electronic means.

A computer's working memory consists of a vast array of cells where every cell has a capacitor and a transistor. The transistor is primarily used to rapidly fill or drain the capacitor of a small electric charge and thus provides us with our two binary representations (1 if full, 0 if empty). Unfortunately, the capacitor cannot hold its charge for long; it will drain away within a few milliseconds of being filled. This is not much use to us because in order to provide a memory we need to maintain state as will as switch states. Fortunately, the transistor can detect how much charge is currently in the capacitor, so if it is above a certain level the transistor can simply refill it. This is achieved through a memory refresh which has to occur at a rate such that capacitors that were filled upon the last refresh cycle still hold enough charge to register for a refill upon the next refresh. Now we have a memory that can maintain state.

Answer 2

RAM is probably the simplest form of memory to understand because the physical representation of the data within memory has a direct correlation with the data itself. RAM is typically made up of billions of individual cells where each cell contains a capacitor and a transistor and each cell can store exactly one bit (a binary digit) of information. The capacitor can briefly store an electrical charge that will drain away after a few milliseconds while the transistor is used to either refill the capacitor or to drain it completely, thus switching its state. A control voltage is used to determine if a sufficient charge exists in the capacitor or not. Since the capacitor will lose any charge, a refresh cycle must be performed before the charge falls below the control voltage. During a refresh, if a capacitor has a sufficient charge, it is refilled by the transistor, otherwise it is allowed to drain.

HDD memory makes use of the magnetic properties of the medium to represent the bits. However, its a bit more complex than simply recording a sequence of positively and negatively charged particles to represent the individual bits of information. For one thing, unless the medium is travelling beneath the read/write heads at a highly consistent rate, there would be no way to differentiate a long series of 1s (or 0s) to any degree of accuracy. Thus the data stream must be interwoven with a timing signal. There are various methods of doing this but, at its simplest level, we can think of the timing signal as being an alternating sequence of 1s and 0s interleaved into the data. Thus the binary value 1101 could be encoded as 10110011, such that the even bits alternate (denoting the timing signal) while the odd bits are the actual data. The actual schemes used are a bit more complex, but they ultimately ensure a high-degree of accuracy with minimum redundancy. But regardless of the encoding used for timing purposes, it would be a mistake to think a binary 1 is written as a cluster of positively charged particles upon the medium and a 0 as a negatively charged cluster. In actual fact it is the flux transitions, whether transiting from positive to negative or from negative to positive, that denote a binary 1, while a non-transition denotes a 0. This is simply because it's much simpler to detect a transition, regardless of its direction, than it is to detect whether the waveform is in the positive or negative phase.

Optical devices such as CD and DVD mediums also employ a timing mechanism encoded within the data stream, however the data is stored much like the punch-cards that were used in days gone by -- as a series of pits and lands. Again, it is the transitions from pit to land or land to pit that denote the individual bits.

Answer 3

Digital computers are nothing more than machines which can read and write binary representations. Those representations can take many forms however it is important to note that only humans interpret binary digits (bits) as being either 1 or 0. It makes sense for us to use digital notation but it makes no sense to a computer; it is just a machine.

Given that a single bit is either 1 or 0, there are many ways we can represent these opposing states. Black and white, on and off, positive and negative, true and false, chalk and cheese; all are equally valid representations to a human, but some (like chalk and cheese) are simply far too abstract for a machine to comprehend. However, a computer still has to use a wide variety of both analogue and digital representations and must be able to convert between the two.

The simplest analogue representation is a switch. Just as we can use a light switch to turn a lamp on and off, we can use a switch to set or unset a binary digit (by allowing electricity to flow or to interrupt the flow). The more switches we use the more binary digits we can physically represent, such that for each additional switch we double the number of "states" we can represent. Although we tend not to use banks of switches on modern computers, they are still in use today on some hardware devices. For instance, your computer's motherboard will undoubtedly have several banks of exposed conductors arranged in pairs. Jumpers can be used to close certain pairs and thus configure the motherboard's "state", enabling or disabling certain optional features. Dual-inline package (DIP) switches are another common example of switches being used to encode modern devices.

A computer has an extremely limited set of "native" operations. The actual number of operations available will vary from system to system, however each specific operation can be encoded in much the same way we can configure a hardware device using DIP switches. Only instead of switches we use CPU registers. One register in particular is used to configure the specific operation we wish to carry out while other registers are used to provide any additional data required by that operation or simply to provide "housekeeping" data for the CPU. Just as the number of operations can vary from system to system, the encodings for each specific operation can also vary. This is why machine code programs intended for one architecture platform won't run on any other platform.

A computer's computational power stems from how quickly it can switch from one operation to the next. If we had to do this manually by setting switches, computers would be extremely slow indeed. Fortunately, we can use electrical energy to automate the process and thus speed things up considerably.

CPU registers work in a similar manner to working memory (RAM) in that each switch (bit) is represented by a capacitor and a transistor working in tandem. The capacitor can hold a small electrical charge while the transistor is used to fill or drain the charge from the capacitor (as well as to "signal" the capacitor's state). However, a capacitor is a bit like a leaky bucket, it can only hold a charge for a short period (a few milliseconds at most). If the charge falls below a critical level, the bit will switch state, thus the transistor must regularly "refresh" the capacitor to maintain state. This is what we mean by memory refresh cycles and the faster we can physically refresh memory, the more time we have to read and write data within each cycle.

Since there are relatively few CPU registers, we can afford to use much larger capacitors (which take longer to drain) with faster transistors than we can afford to use in working memory. This ensures processing speed is as high as possible. RAM contains billions of much smaller/slower capacitor/transistor pairs hence high-performance RAM is so expensive. High-performance graphics cards and other devices that rely on high-performance RAM provide their own -- at enormous expense!

In addition to RAM and CPU registers, your computer will also use a variety of ROM (read-only memory) chips. These chips can maintain state without electrical power and are used to provide the basic programming required to initialise devices at power up. The BIOS (basic input/output system) programming and data is provided via a CMOS (complementary metal-oxide semiconductor), a type of EPROM (erasable programmable ROM) that maintains state via an accumulator (a rechargeable battery). The BIOS essentially provides all the services required to initialise the computer, enumerate its core devices and locate the boot loader which takes care of the remainder of the boot process.

Working memory obviously cannot maintain state without electrical energy. This is known as volatile memory. In order to maintain state during a power outage, we must store binary data somewhere else, using a non-volatile storage medium. For this we have a number of options including solid state drives, hard-disk drives, optical discs (CD, DVD, HD, BluRay, LaserDisc, etc), SD cards and magnetic tape. Collectively we refer to these devices as mass-storage devices. Each device has a different method of representing binary data but essentially uses the same principal of opposing states, converting electro-mechanical, magnetic, optical or other analogous representations into digital (binary) representations which can then be decoded to reproduce the original data.

Other ways we can represent and store binary data include the use of QR (quick-response) codes, barcodes, grey codes and radio transmissions. Indeed, the sheer number of ways we can represent binary data in a form that a computer can physically interpret is limited only by our imaginations.