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.