Least significant bit (LSB)

Also called: low-order bit, rightmost bit, bit 0

The rightmost bit of a binary number, bit 0, with weight 1. It alone decides whether the number is odd (LSB 1) or even (LSB 0).

The least significant bit (LSB) is the rightmost bit of a binary number. It's bit 0, with weight 2⁰ = 1, so flipping it changes the value by the smallest possible amount.

Useful facts about the LSB:

Odd or even. Every other weight (2, 4, 8, …) is even, so the LSB alone decides: LSB 1 means odd, LSB 0 means even.
First out of repeated division. Dividing by 2 asks "is it odd?", so the first remainder in repeated division is the LSB.
Where addition starts. Column addition begins at the LSB and carries move left toward the MSB. In an adder circuit, the carry chain starts at bit 0's carry-in, C0 (see ripple carry adder).
Grouping anchor. When converting binary to hex or octal, you group bits starting from the LSB. See binary hex conversion.

Unlike the MSB, the LSB doesn't depend on the width: adding leading zeros never moves it.

Worked example

Example

Odd or even at a glance

Look only at the last bit.

1.
1011₂: LSB 1, so odd. Check: 8 + 2 + 1 = 11.
2.
1010₂: LSB 0, so even. Check: 8 + 2 = 10.
3.
1101101100₂: LSB 0, so even, with no conversion needed. (It's 876.)

Common mistakes

Reading repeated-division remainders top-down. The first remainder is the LSB, so the bits are read bottom-up.
Calling the LSB bit 1. Bit numbering starts at 0.

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Least significant bit (LSB) is taught in Number Systems.

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