New Number Methods

Number Theory Level 1

You need to answer the question in bold text. However, you only have one clue: 10110 = 22. What does 111111111 equal?

3 solutions

§Martie On Brilliant
Mar 20, 2021

As $10110$ $=$ $22$ is a conversion of binary to base 10, we can model the problem using Python: $\\$

print(str(int("111111111", 2)))
# Returns 511

$111111111$ converted to base 10 is $\boxed{511}$

Vishruth K - 2 months, 3 weeks ago

Saya Suka
Mar 19, 2021

111111111 = 1000000000 - 1
Answer = 2^9 - 2^0 = 512 - 1 = 511

Interliantiful!

Vishruth K - 2 months, 3 weeks ago

Vishruth K
Mar 19, 2021

10110 in binary equals 16 + 4 + 2 = 22. 111111111 in binary equals 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 511. Thus, the answer is 511 .