Number system conversion practice with answers
Number system conversion practice for binary, octal, decimal and hexadecimal: problems appear instantly, you type your answers and get them checked – with the solution and working. Print it as a worksheet with an answer key if you like.
Source: Wikipedia – Positional notation. Updated: .
How it is calculated
How the practice worksheet works
Choose the problem type (for example decimal → binary or binary → hexadecimal), the number range and how many problems you want. The worksheet appears immediately. Type your answers and tap “Check”: correct answers get a tick, and for wrong ones the answer and the working are shown. “Show answers” reveals every answer at once. “New problems” rolls a new worksheet; the settings and the variant are part of the link, so a whole class can open the same sheet.
The methods at a glance
- Decimal → binary, octal or hexadecimal: divide by the target base, write down the remainder and continue with the quotient until 0 is left. Read the remainders from bottom to top. Example: 182 ÷ 2 = 91 remainder 0, 91 ÷ 2 = 45 remainder 1 … gives 1011 0110.
- Binary, octal or hexadecimal → decimal: multiply each digit by its place value (a power of the base) and add. Binary: 1011 0110 = 128 + 32 + 16 + 4 + 2 = 182. Hex: B6 = 11 · 16 + 6 = 182.
- Binary ↔ hexadecimal: split the bits into groups of four from the right – each group is exactly one hex digit (1011 = B, 0110 = 6). For octal, group three bits at a time.
Which range fits?
Up to 15 needs four bits – a good start, and the range of one hex digit. Up to 255 is one byte (eight bits), the usual level in computer science classes and the range of each part of an IPv4 address or an RGB colour value. 4,095 (12 bits) and 65,535 (16 bits) train longer numbers and the groups of four in hexadecimal. Numbers are never smaller than an eighth of the range, so you do not get only tiny values.
Printing as a worksheet
“Print” outputs only the worksheet with empty answer lines and a name line; everything else on the page is hidden. With the option to add the answer key, a second page with all answers follows for the teacher. To get a PDF, choose “Save as PDF” in your browser’s print dialog. Nothing is uploaded; the problems are generated in your browser.
To convert a single number, use the number base converter with working – it also handles fractions, negative numbers and every base from 2 to 36.
Frequently asked questions
How do I convert a decimal number to binary?
Divide the number by 2 again and again and write down the remainders. Read from bottom to top, the remainders are the binary number. Example: 13 ÷ 2 = 6 remainder 1, 6 ÷ 2 = 3 remainder 0, 3 ÷ 2 = 1 remainder 1, 1 ÷ 2 = 0 remainder 1 gives 1101.
How do I convert binary to decimal?
Write the place value above each digit (from the right 1, 2, 4, 8, 16 …) and add up the values of the digits that are 1. Example: 1101 = 8 + 4 + 1 = 13.
How does binary to hexadecimal work?
Group the bits in fours from the right. Each group is a hex digit from 0 to F: 1010 = A, 1011 = B, 1111 = F. So 1011 0110 becomes B6.
Which digits does hexadecimal use?
Sixteen: 0 to 9 and the letters A to F for the values 10 to 15. Upper or lower case does not matter when you type, and prefixes such as 0x are accepted.
Are there answers to the problems?
Yes. “Check” shows the answer and the working for every wrong response, and “Show answers” reveals all of them. When printing, you can add the answer key on a separate page.
Can I save the worksheet as a PDF?
Yes: tap “Print” and choose “Save as PDF” in the print dialog. The sheet has empty answer lines and a name line; the answer key goes on a second page if you ask for it.
Which problems suit a computer science class?
Start with decimal ↔ binary up to 15 or 255, then binary ↔ hexadecimal and “Mixed”. The range up to 65,535 lets you practise 16-bit values such as addresses and colour codes.
Sources and legal basis
As of: · Editorial policy
Related tools
- Number base converter with stepsConvert between binary, octal, decimal, hex and any base from 2 to 36 – with full working, fractions, repeating digits and two’s complement (8–64 bit).
- Text to binary converter (and binary to text)Convert text to binary, hex, decimal or octal and translate binary back to text – with UTF-8 for accents and emoji, right in your browser, nothing uploaded.
- Exponent calculator with stepsCalculate powers, nth roots and logarithms with any base – step-by-step, with negative and fractional exponents, ln, log and scientific notation.
- Printable math worksheets for grades 1–6Free math worksheets with answer keys for grades 1–6: math facts, times tables, fractions, decimals, percentages, telling time, money. Same link, same sheet.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Center of mass calculator for up to four massesCenter of mass calculator: x and y coordinates of the centre of mass of up to four point masses – or the centroid of a composite shape from its part areas.
- Clock Angle CalculatorClock angle calculator: the angle between the hour and minute hand for any time, with the formula |30h − 5.5m|, the smaller and larger angle and every step.
- Pneumatic cylinder force calculator with load factor and air consumptionPneumatic cylinder force calculator: extend and retract force from bore, rod and pressure, usable load with SMC load factor, minimum bore and air consumption.
- Doppler Effect CalculatorDoppler effect calculator for sound: heard frequency for a moving source and observer, shift in Hz and semitones, with a pass-by table and steps.