Technology is the largest of the three areas, taking 11 topics of the 23 calculation topics. Most of it is calculation tied to the basics of IT: availability, base conversion, logical operations and so on.
Eight of these topics are rated "highest" for question frequency, so covering this area alone lifts your score on calculation problems considerably.
💻 Technology (11 topics)
#1 Availability (series system)
A configuration in which several devices are lined up along a single path, and every one of them has to be working.
Overall availability = Availability of device A × Availability of device B- Availability: The probability that the system is operating normally (0.0 to 1.0)
Solution steps
- Turn each availability figure into a decimal
Convert the percentages into decimals.
Example: 90% → 0.9 - Multiply the figures together
Multiply the availability of every device.
Example: 0.9 × 0.8 = 0.72
Common mistakes
- Adding the availability figures together
Multiplying probabilities is what gives you the probability that things happen at the same time. Adding them can exceed 1, which cannot be a probability.
Exam pointers
- A series diagram shows the devices lined up in a single row.
- You can use the fact that the result is always smaller than any individual device's availability as a sanity check.
How to remember
"A series is a shared fate. One falls, they all fall."
"Checkpoints on a single road. You only reach the goal by passing every one."
#2 Availability (parallel system)
A configuration with several devices held as spares, which keeps running as long as any one of them is working.
Overall availability = 1 - (1 - Availability A) × (1 - Availability B)- Failure rate: The probability that the system is down (if availability is 0.9, the failure rate is 0.1)
Solution steps
- Find each failure rate
Subtract the availability from 1.
Example: for an availability of 0.9, 1 - 0.9 = 0.1 - Find the probability that all of them fail
Multiply the failure rates together.
Example: 0.1 × 0.1 = 0.01 - Subtract that from the whole (1)
Every case other than "all down" means the system is running.
Example: 1 - 0.01 = 0.99
Common mistakes
- Simply multiplying the availability figures
That is the calculation for a series (no spares). - Forgetting to subtract from 1 at the end
You have answered with the probability that everything fails.
Exam pointers
- A parallel diagram shows the devices stacked one above the other.
- The result is always larger than any individual device's availability.
How to remember
"For a parallel system, take the chance that everyone falls asleep and subtract it from a wide-awake 1."
"As long as one of them is still standing, the system is alive."
#3 MTBF / MTTR
Measures of the interval between failures (the healthy time) and the time taken to repair them (the time spent in bed).
Availability = MTBF ÷ (MTBF + MTTR)- MTBF: Mean time between failures. The average time it runs without breaking.
- MTTR: Mean time to repair. The average time spent under repair after a failure.
Solution steps
- Work out the total time
Add MTBF and MTTR together.
Example: MTBF = 900 hours and MTTR = 100 hours gives 1,000 hours in total - Work out the share that is healthy time
Divide MTBF (the healthy time) by the total.
Example: 900 ÷ 1000 = 0.9 (90%)
Common mistakes
- Putting only MTTR in the denominator
MTBF ÷ MTTR gives you a ratio — how many times longer the healthy time is than the repair time. - Getting the meanings of MTBF and MTTR the wrong way round
You have mixed up what the F and the R stand for.
Exam pointers
- For "how do you raise availability?", the answer is either to make MTBF larger or to make MTTR smaller.
- Adding maintenance staff shortens MTTR (repair time); switching to higher-quality parts lengthens MTBF (the interval between failures).
How to remember
"Divide the healthy time by the whole life. That is availability."
"B is for Between, R is for Repair. Time until it breaks, and time until it is fixed."
#4 Base conversion (binary ⇔ decimal)
The technique for rewriting numbers between the decimal system people use and the ones and zeros (binary) a computer uses.
Decimal = Σ (digit × its power-of-two weight)- Weight: The value of each place (from the right: 1, 2, 4, 8, 16, 32, 64, 128...)
Solution steps
- Prepare the power-of-two weight cards
Lay out cards written 1, 2, 4, 8, 16, 32... doubling each time, starting from the right.
Example: say you are looking at the binary number 101101 - Add the cards where the bit is 1
Sum only the weights in the places where the binary digit is 1.
Example: 32(1) + 8(1) + 4(1) + 1(1) = 45
Common mistakes
- Starting the weights at 0 or at 2
The first place starts at 2⁰, which is 1.
Exam pointers
- Writing the table "128 | 64 | 32 | 16 | 8 | 4 | 2 | 1" in the margin of the question paper makes you unbeatable.
- An even binary number always ends in 0 and an odd one always ends in 1. That alone can sometimes narrow the choices down.
How to remember
"Just add up the weight cards (1, 2, 4, 8...). Binary is the sum of its weights."
"Binary 101 is 5, and 1010 is 10."
#5 Base conversion (hexadecimal)
A technique that uses the digits 0-9 plus the letters A-F to write binary numbers short and tidy.
One hexadecimal digit = four binary bits- Hexadecimal characters: After 0-9 come A(10), B(11), C(12), D(13), E(14), F(15)
Solution steps
- Split the number into groups of four bits
Divide the binary number into chunks of four, starting from the right (the low digits).
Example: 111011 → split into 0011 / 1011 (pad the left with zeros if you are short) - Convert each chunk into hexadecimal
Convert each four-bit chunk on its own.
Example: 0011 = 3, and 1011 = 11, which is B. Together that is "3B".
Common mistakes
- Splitting the binary number into groups of three bits
That is the rule for octal. Hexadecimal is always four bits. - Miscounting from A(10)
Counting on your fingers can slip, so you end up with A = 11 or similar.
Exam pointers
- If a colour-code question comes up (#RRGGBB), remember that each colour is two hexadecimal digits, which is eight bits.
- "Binary to hexadecimal" is the easiest place in the Technology area to raise your score on the IT Passport.
How to remember
"One hex digit, four binary siblings."
"A(10), B(11)... and F(15) at the end. The letters are the bridge into two digits."
#6 Logical operations (AND/OR/XOR)
Calculations that take a combination of 0s and 1s and derive a new 0 or 1 from it, using rules like "and" and "or".
Bitwise logical operations (based on the truth table)- AND (logical product): 1 only when both are 1, otherwise 0 (the strict condition)
- OR (logical sum): 1 when either one is 1, and 0 only when both are 0 (the lenient condition)
- XOR (exclusive or): 1 when the two values differ, 0 when they are the same (spot the odd one out)
Solution steps
- Line the digits (bits) up vertically
Write the two binary numbers one above the other.
Example: line up 1010 and 1100 - Apply the given rule one digit at a time
For AND ask "are both 1?"; for OR ask "is either one 1?".
Example: for AND, the first digit is 1 and 1 so it is 1; the second is 0 and 1 so it is 0...
Common mistakes
- Confusing XOR with OR
OR is also 1 when both are 1, but XOR gives 0 when both are 1, because they are the same.
Exam pointers
- To force particular bits to 0 you use AND (think of multiplying by 0); to force them to 1 you use OR (think of adding 1).
- XOR has the property that applying it twice with the same value returns the original, so it often appears in simple explanations of encryption.
How to remember
"AND is multiplication (1×1=1); OR is addition (anything 1 or more comes out as 1)."
"XOR is 1 on a mismatch. Differ, and it stands up."
#7 Data transfer time
Working out how many seconds it takes to send data of a given size over a line of a given speed.
Transfer time (s) = Data size (bits) ÷ (Line speed (bps) × Transmission efficiency)- Data size: The size of the file (e.g. 200MB). You have to convert it into bits before calculating.
- Line speed: The number of bits that can be sent per second (bps = bits per second)
- Transmission efficiency: The share of the line that actually carries data (e.g. 0.8)
Solution steps
- Get everything into bits
Multiply the file size in bytes (B) by 8 to turn it into bits.
Example: 100MB × 8 = 800M bits - Calculate the effective speed
Multiply the line speed by the transmission efficiency (%).
Example: 100Mbps × 0.5 (50%) = 50Mbps - Do data size ÷ speed
From there it is the same as distance ÷ speed.
Example: 800M bits ÷ 50Mbps = 16 seconds
Common mistakes
- Carrying on without multiplying by 8
You have not noticed that line speed (bps) and file size (B) use different units. - Dividing by the transmission efficiency instead of multiplying
Efficiency is a factor that reduces performance, so the speed should come out smaller.
Exam pointers
- Almost all questions have you treat 1G (giga) as 1,000M (mega), not 1,024.
- You may be asked the reverse — "how much data can be transferred?" rather than "how long does the transfer take?" — but the formula has the same shape.
How to remember
"Bits and bytes: never forget the factor of 8."
"1,000× between mega and giga, 8× between bits and bytes."
#8 Image / audio data size
How to calculate the size of digital data. An image comes from resolution × colour depth; audio comes from sampling frequency × quantization bit depth.
Image size = Width × Height × Colour depth ÷ 8- Resolution: The number of pixels across and down
- Colour depth: The number of bits per pixel (24-bit colour, for example)
How to remember
"Width × height × colour, then divide by 8. Bits become bytes by dividing by 8."
#9 Availability (composite system)
A more complex configuration that mixes series and parallel, closer to a real system.
Overall availability = combine the availability of each part, stage by stageSolution steps
- Find the parallel parts and treat each as one block
Start by calculating the small blocks that are in parallel.
Example: if a parallel part works out to 0.99, treat it as a single device with an availability of 0.99 - Multiply the whole thing as one series path
Multiply from end to end, including the block you rewrote.
Example: 0.9 (device 1) × 0.99 (parallel block) = 0.891
Common mistakes
- Trying to multiply every figure at once
There is a parallel part, so plain multiplication alone will not solve it.
Exam pointers
- A diagram shaped like A - (B||C) - D, bulging only in the middle, is the standard form.
- Rounding the intermediate decimals too aggressively introduces error, so keep the figures exact until the end.
How to remember
"For a composite system, find the cluster and pack it into a box (a single availability figure)."
"Solve the parallel part first, then redraw it as a single road (a series)."
#10 Yield / defect rate
Metrics for what share of the raw materials and parts you put in come out as good products (yield), and what share come out defective (defect rate).
Yield = Number of good products ÷ Number put in × 100- Number of good products: The number of products that met the quality standard
- Number put in: The number of raw materials and parts fed into the process
How to remember
"Yield multiplies. The more stages there are, the more it falls."
#11 Memory / address calculation
How to calculate the range of memory a CPU can address (the address space), and the number of address bits you need.
Address space = 2^(number of address bits)- Number of address bits: The width of the address bus (32 for a 32-bit CPU)
How to remember
"n bits lets you address 2 to the power of n locations."
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