how many bits would you need if you wanted to count up to the decimal number 1000?

To count up to the decimal number 1000, you need at least 10 bits. This is because 210=10242^{10}=1024210=1024, which is the smallest power of 2 greater than 1000, allowing you to represent all numbers from 0 up to 1000 (and beyond, up to 1023) in binary form

. The general formula to find the number of bits nnn required to represent a decimal number NNN is:

n=⌈log⁡2(N)⌉n=\lceil \log_2(N)\rceil n=⌈log2​(N)⌉

For N=1000N=1000N=1000,

log⁡2(1000)≈9.97\log_2(1000)\approx 9.97log2​(1000)≈9.97

Rounding up gives n=10n=10n=10 bits

. Thus, 10 bits are sufficient to count from 0 up to 1000 in binary.