Coding Grandmaster · project 13 of 46 · premium, free for now

Seeing the bits

Print each of 5, 12 and 255 as 8 binary digits, and write count_ones(n) that counts the 1 bits using & and >>.

Learn

Inside the computer every whole number is a row of bits. In Python, f"{n:08b}" shows n as 8 binary digits. n & 1 looks only at the last bit (1 if odd), and n >> 1 slides all bits one place right, which halves the number. A loop that checks the last bit and shifts can count how many 1s a number has, called its popcount.

Your task

Print each of 5, 12 and 255 as 8 binary digits, and write count_ones(n) that counts the 1 bits using & and >>.

Stretch challenge

Write the same thing with only the trick n = n & (n - 1) inside the loop.

← Counting in other bases One-line bit tricks →

Python

Press Run to see what your program prints.

Keep going in Coding Grandmaster

One-line bit tricks

Write is_power_of_two(n) using n & (n - 1), is_odd(n) using n & 1, and print the powers of two up to 200 using a list comprehension.

Start →15

XOR magic

Swap a and b with three XOR lines (no temporary variable), and write lonely(numbers) that returns the number that appears only once by XOR-ing everything together.

Start →16

Set, clear and toggle

Write set_bit(n, i), clear_bit(n, i), toggle_bit(n, i) and test_bit(n, i) (True or False) using shifts and bitwise operators.

Start →17

Every subset

Write subsets(items) returning a list of every subset as a list, in the order of the counter 0 to 2^n − 1, using bit tests. Print how many subsets four items have, and the subsets of two items.

Start →18

Permission flags

With READ = 4, WRITE = 2 and EXEC = 1, write grant(perms, flag), revoke(perms, flag), has(perms, flag) and describe(perms) which returns text like r-x (r, w and x, or - for a missing one).

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Practise the idea

💡 Play Binary Bits

Switch bit values to make the decimal number shown on screen.

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FAQ

Seeing the bits: common questions

I am stuck. What can I do?

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