Base Conversions Flashcards

1️⃣ Familiarise yourself with the flashcards:

Look through all the flashcards to see what's on both sides.
Make sure you understand the information on each card. If something's unclear, click the link to the revision notes at the bottom of the page for more details.

2️⃣ Test yourself:

Look at the question or prompt on each card and try to remember the answer before flipping it over.
Check the answer and make a note of any cards you find challenging and need to go over more.

3️⃣ Consistently Review and Practice:

Use spaced repetition: spend more time on the cards you struggle with and go over them more often.
Regularly review all the flashcards to help you better understand and retain the information over time.

Note: We may include questions that have multiple correct answers. It's useful to remember specific examples to understand these concepts better.

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What does the base of a number system mean?

It is how many different digits the system uses. Base 2 uses 0 and 1; base 16 uses 0-9 and A-F.

Write place values 1, 2, 4, 8, 16 under the bits. Add the values where the bit is 1.

11, because 1011 has 8 + 2 + 1.

Find the largest value from 1, 2, 4, 8, 16 that fits. Put 1 there, subtract it, and repeat. Put 0s in the other places.

1101, because 13 = 8 + 4 + 1.

From right to left, use place values 1, 16, 256, 4096. Multiply each hex digit by its place value (A=10 to F=15) and add.

47, because 2F = 2 x 16 + 15.

Split the binary into groups of 4 bits from the right. Add leading zeros if needed, then convert each group to one hex digit.

D6, because 1101 is D and 0110 is 6.

Replace each hex digit with its 4-bit binary form. For example, 7B becomes 0111 1011.

Divide by 16 and note the remainder. Keep dividing the result by 16. Read the remainders from last to first, using A-F for 10-15.

3C, because 60 / 16 = 3 remainder 12, and 12 is C.