Powers of 2, from 2⁰ to 2³²

Powers of 2 turn up in computing (bytes, memory, colour depth), in doubling problems and in mental math shortcuts. Here is the full table, and the one fact that lets you rebuild it from memory.

The table

The shortcut: 2¹⁰ ≈ 1,000

2¹⁰ is 1,024, just over a thousand. So every ten powers of 2 add roughly three zeros:

To get any power, split the exponent into tens and a remainder. 2²³ = 2²⁰ × 2³ ≈ 1 million × 8 = 8 million (exactly 8,388,608). 2³² = 2³⁰ × 2² ≈ 4 billion (exactly 4,294,967,296).

The estimate always runs a little low, and the gap grows: it's 4.6% short at 2²⁰ and 6.9% short at 2³⁰.

Where you'll see them

• 256 (2⁸): values in one byte, and levels per colour channel.
• 1,024 (2¹⁰): bytes in a kibibyte.
• 65,536 (2¹⁶): values in two bytes.
• 4,294,967,296 (2³²): values in a 32-bit integer, and why older 32-bit systems topped out at 4 GB of memory.

Doubling in your head

Climbing the table is just repeated doubling, and doubling a big number is easiest left to right: 8,192 doubled is 16,000 + 384 = 16,384. If doubling and halving feel slow, the rest of mental math will too. R3CK0N's timed multiplication drill builds that speed.