You would need 10 bits to count up to the decimal number 1000.

Quick Scoop: Why 10 Bits?

Think of bits as tiny switches that can be 0 or 1.
With nnn bits, you can represent numbers from 0 up to 2n−12^n-12n−1. We want to be able to count up to 1000 , so we need the smallest nnn such that:

2n−1≥10002^n-1\ge 10002n−1≥1000

Let’s check nearby powers of 2:

  • 29=5122^9=51229=512 → can count only up to 511 (not enough).
  • 210=10242^{10}=1024210=1024 → can count up to 1023, which covers 1000.

So 9 bits are too few, but 10 bits are enough, meaning you need 10 bits to count up to (and include) 1000.

A Tiny Story Version

Imagine a digital odometer with little windows that show only 0s and 1s instead of digits 0–9.

  • With 9 windows (bits), the biggest pattern you can show is 111111111, which corresponds to 511 in decimal.
  • You try to display 1000, but you run out of patterns.
  • You add one more window, making it 10 bits.
    Now your maximum pattern is 1111111111, which corresponds to 1023 — plenty of room to include 1000.

So, once that 10th bit is added, your counter can happily go all the way up to 1000.

TL;DR

To have the ability to count from 0 up to the decimal number 1000, you need 10 bits.

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