# Definition:Least Significant Digit

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## Definition

Let $b \in \Z: b \ge 2$ be a number base

Let $n$ be a number which is reported to $r$ significant figures, to base $b$, that is:

- $n = d_1 \times b^k + d_2 \times b^{k - 1} + \dotsb + d_{r - 1} \times b^{k - r + 2} + d_r \times b^{k - r + 1}$

where:

- $d_1, d_2, \dotsc, d_r$ are the significant figures of $n$
- $b^k$ is the largest power of $b$ less than or equal to $n$.

Then the digit $d_r$ is known as the **least significant digit** of $n$.

Note that the usual situation is when $b = 10$, but in the field of computer science, binary is usual.

## Also known as

The **least significant digit** can also sometimes be seen as **least significant figure**.

When $n$ is expressed in binary notation, the **least significant digit** is often referred to as the **least significant bit** and abbreviated **lsb** or **l.s.b.**