CompTIA Tech+ IT Concepts: Computing Basics, Number Systems, Units and Troubleshooting

Every computer, from a smartwatch to a data-center server, does four jobs: it takes in data (input), works on it (processing), presents a result (output) and keeps data for later (storage). Together these are often called the IPOS cycle, and classifying a device or action means asking which of the four jobs it is doing at that moment.

One device usually performs all four functions in sequence. A fitness tracker counts wrist movements with its motion sensor (input), works out the day's step total and checks it against a saved goal (the goal is in storage; the calculation and the check are processing) and then buzzes and shows a message when the goal is reached (output). When you classify, focus on the single action described: what the user sees, hears or holds is output; calculating, comparing and deciding are processing.

Storage is the function that keeps data after the device is switched off; the working memory (RAM) used while you edit a file does not. RAM is volatile: it is fast and holds the programs and data in use right now, but it is cleared when power is lost. Drives such as SSDs, hard disk drives, USB flash drives and cloud storage are non-volatile: data written there remains until it is deleted.

This is why saving matters. While you edit a document, the changes live in RAM. Saving writes them to storage. If the power fails before you save, the unsaved changes in RAM are lost, while everything already saved on the drive, a USB stick or a backup is still there after the restart.

Binary is the base-2 notational system computers use internally: it has only two digits, 0 and 1, and each digit is a bit. Decimal is the everyday base-10 system with the digits 0 to 9. In any base, each place is worth the base times the place to its right, so in binary the place values double from the right: 1, 2, 4, 8, 16, 32, 64, 128.

Binary to decimal

Write the place values under the digits and add the places that hold a 1. For example, 1101 has 1s in the 8, 4 and 1 places, so it equals 8 + 4 + 1 = 13. For the 8-bit value 10100000, the 1s sit in the 128 and 32 places, giving 160. All eight bits set (11111111) is 255, the largest value one byte can hold, which is why a byte has 256 possible values (0 to 255).

Decimal to binary

Subtract the largest place value that fits, mark that place with a 1, and repeat with what is left. For decimal 22: 16 fits (6 left), 8 does not, 4 fits (2 left), 2 fits (0 left), 1 does not, giving 10110. Check your answer by converting it back.

Reading the digits in the wrong direction is the most common error. The rightmost bit is always worth 1, and the value grows towards the left.

You can identify a notational system from its digit set: the highest digit is always one less than the base. Octal (base 8) uses 0 to 7; hexadecimal (base 16) uses 0 to 9 and then the letters A to F for the values 10 to 15.

Any letter from A to F in a number tells you it is hexadecimal, because no other common system uses letters. A network adapter's MAC address, such as 00-1A-2B-3C-4D-5E, is six pairs of hex digits, one pair per byte, for 48 bits in total. A web color such as #FF8800 is three pairs giving the red, green and blue intensities from 00 (none) to FF (full, 255).

Octal fits Linux permissions because each permission group (owner, group, others) is three bits, one each for read, write and execute, and three bits hold exactly eight values, 0 to 7. Read is worth 4, write 2 and execute 1, so 6 means read and write (110) and 7 means all three (111). Sometimes a value is labelled by base number instead of name; base 16 is hexadecimal, base 8 is octal, base 2 is binary and base 10 is decimal.

Hexadecimal is popular in IT because one hex digit stands for exactly four bits: four bits give 16 combinations, and hex has 16 digits. So one byte (8 bits) is always exactly two hex digits, which makes long binary values much easier to read and type.

To convert binary to hex, split the bits into groups of four starting from the right, convert each group on its own, and keep the groups in order. For 11010011: 1101 = 8 + 4 + 1 = 13 = D, and 0011 = 2 + 1 = 3, so the result is D3. To go the other way, expand each hex digit back into its four bits: 2F becomes 0010 1111.

Octal works the same way with groups of three bits. Decimal is the odd one out: its digits do not line up with whole groups of bits, which is why conversions to and from decimal need place-value arithmetic.

To compare or match numbers written in different bases, convert them all to one base (usually decimal) first; the digits alone are misleading. The same digits mean different amounts in different systems: 21 is twenty-one in decimal, but 2 × 8 + 1 = 17 in octal and 2 × 16 + 1 = 33 in hexadecimal.

Each place in a number is worth the base raised to a power: in octal the places are 1, 8, 64; in hexadecimal they are 1, 16, 256. A useful rule is that 10 in any base equals the base itself: binary 10 is 2, octal 10 is 8, hexadecimal 10 is 16.

A worked example: which is larger, octal 120 or hexadecimal 4F? Octal 120 = 1 × 64 + 2 × 8 + 0 = 80. Hexadecimal 4F = 4 × 16 + 15 = 79. Octal 120 is larger by one, even though 4F contains a letter and 120 has more digits: neither the digit count nor the letters decide the size until both values are in the same base.

Data size is measured in bytes, where one byte is 8 bits and a bit is a single 0 or 1. Larger storage units step up by about a thousand each time:

Drive makers use exact powers of ten (1 GB = 1,000,000,000 bytes), while operating systems often count in powers of two (1,024 bytes per kilobyte). The 1,024 figures are formally called kibibytes, mebibytes and so on; both conventions exist, and the difference explains why a new drive shows slightly less capacity than its label. For estimates and comparisons, a thousand per step is close enough.

To convert, divide by about a thousand to move up one unit and multiply to move down. Always read the unit before the number: 6,000 MB is about 6 GB, which is far smaller than 1 TB, even though 6,000 looks like a bigger number.

Throughput is how much data moves per second, and it is measured in bits per second, written with a lowercase b: bps, Kbps, Mbps, Gbps and Tbps. Like storage units, each prefix is a thousand times the one before (1 Gbps = 1,000 Mbps = 1,000,000 Kbps). Home internet plans are usually sold in Mbps or Gbps; Tbps speeds appear mainly in backbone and data-center links. (The official objectives spell Tbps out as "terabytes per second", but the lowercase b means bits, so Tbps is terabits per second.)

Bits versus bytes

Network speeds are quoted in bits; file sizes and many download windows show bytes (MB/s, uppercase B). Because a byte is 8 bits, divide a speed in Mbps by 8 to get MB/s. A 1 Gbps (1,000 Mbps) connection therefore moves at most about 125 MB/s of file data; the two figures describe the same speed in different units.

Estimating transfer time

1. Convert the file size to bits: multiply bytes by 8.
2. Match the prefixes (for example, turn GB into MB, or Mb into Gb).
3. Divide the size by the speed to get seconds.

Example: a 5 GB file over a 500 Mbps link. 5 GB ≈ 5,000 MB; × 8 = 40,000 Mb; 40,000 ÷ 500 = 80 seconds, a little over a minute. Using 1,024 instead of 1,000 changes the answer only slightly. Forgetting the factor of 8 makes the estimate eight times too fast.

To compare speeds written with different prefixes, convert them to one unit first: 2,000,000 Kbps is 2,000 Mbps, which is faster than 1.5 Gbps (1,500 Mbps).

Processing speed is a processor's clock frequency, the number of cycles it completes each second, measured in hertz (Hz). Modern laptop and desktop CPUs run at a few gigahertz (GHz, billions of cycles per second); older or smaller chips are often quoted in megahertz (MHz). (Memory speeds are now usually quoted in MT/s, megatransfers per second, rather than MHz.) 1 GHz = 1,000 MHz, so 2,800 MHz equals 2.8 GHz, which is slower than 3.1 GHz despite the bigger number.

Keep the three kinds of measurement apart:

A quick check: hertz means a processor, "per second" with bits means a connection, and bytes alone mean an amount of stored data.

The CompTIA troubleshooting methodology is a fixed sequence of steps for solving any IT problem, and its order is the point: each step depends on the one before it. The Tech+ objectives list the six step headings plus researching the knowledge base or internet; the detail added under steps 1 and 3 below (questioning the user, duplicating the problem, forming a new theory or escalating) comes from CompTIA's general methodology as published in its A+ objectives, and it is how each step is carried out in practice.

1. Identify the problem. Gather information, question the user, identify the symptoms, determine what has changed recently and, if possible, duplicate (reproduce) the problem. Reproducing a fault to see it for yourself belongs to this step, not to testing, because no cause is suspected yet; for example, asking a user to open the app that keeps freezing while you watch.
2. Establish a theory of probable cause (question the obvious). Propose the most likely cause, starting with simple, common ones: is it plugged in, switched on, connected? If the cause is not obvious, research the knowledge base or the internet, if applicable, for example by searching a vendor forum for the stop code shown on a blue screen.
3. Test the theory to determine the cause. Try something that confirms or rules out the suspicion, such as connecting a known-good monitor to rule the screen in or out. If the theory is confirmed, move on. If not, establish a new theory, or escalate to someone with more knowledge, access or authority when you cannot confirm a cause yourself.
4. Establish a plan of action to resolve the problem and implement the solution. Decide how and when to fix it with the least disruption (for example, arranging a maintenance window for a fix that interrupts users), then carry it out.
5. Verify full system functionality and, if applicable, implement preventive measures. Confirm everything works, not just the symptom that was reported, and take steps so the problem does not recur, such as scheduling a weekly disk cleanup so a drive does not fill up again.
6. Document findings/lessons learned, actions and outcomes. Record the cause, what you did and the result, typically in the help-desk ticket, so the next technician can solve it faster.

The steps that are easiest to confuse:

Documentation is always the last step, and the final three run in a fixed order: implement, verify, document.