What are the position values in an 8-bit binary octet, and why are they important?

From left to right the eight bit positions are worth 128, 64, 32, 16, 8, 4, 2, 1 (each is 2ⁿ); memorizing them lets you convert octets by hand.

* Each bit position is worth 2ⁿ — double the position to its right. Memorize 128 64 32 16 8 4 2 1. *

Binary (Base 2) position values in an octet:

Key memorization: 128, 64, 32, 16, 8, 4, 2, 1

Calculation: Each position = 2^n where n is the bit position

• 2⁷ = 128, 2⁶ = 64, 2⁵ = 32, 2⁴ = 16
• 2³ = 8, 2² = 4, 2¹ = 2, 2⁰ = 1

Range of an octet: 0 (00000000) to 255 (11111111)

Go deeper:

• The binary number system — Khan Academy — how each bit's power-of-two place builds up a value.
• Wikipedia — Binary number — base-2 place values and arithmetic in depth.