Definition:Most Significant Digit

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 $d_1$ is known as the most 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 most significant digit can also sometimes be seen as most significant figure.

When $n$ is expressed in binary notation, the most significant digit is often referred to as the most significant bit and abbreviated msb or m.s.b.

Also see

• Definition:Least Significant Digit