In a nutshell: Normalized binary floating point requires the
mantissa to start with digit $1$. When there is an underflow on the
exponent, the computation may be saved, at the expense of precision,
by allowing the mantissa to start with some leading $0$ in what is
called subnormal or denormalized numbers.
It is always a bit chancy to guess the intended meaning of a statement
without enough context.
I am not sure either of what you means by
when we adopt a normalised representation, our range is smaller than
in a unnormalised representation.
With these disclaimers, here is my understanding.
A first point to note is that the meaning of qualifier normalized
depends on context. In scientific notation, wich is close to floating
point, it means that the mantissa is represented with a single
non-zero digit before the decimal point, for example $2.718\times
The definition is different in the IEEE standards for floating points.
They specify the number of digits used for the mantissa, with no
leading $0$, and with no decimal point (implying it is immediately
right of the last digit which can be $0$).
One characteristic of normalized binary representation is that the
mantissa (called "significand"or "coefficient" in the IEEE standard).
always start with a digit $1$. This gives optimal precision with the
mantissa (though the ending $0$'s may not be significant), and can
save one bit, since a leading $1$ that is always present does not need
to be represented.
However the is a provision for representing subnormal numbers
(also called denormal or denormalized) which, as the names
indicates, are not normalized.
When there is a need to represent a number such that it requires an
exponent smaller than the possible minimum, the normalized computation
will cause an underflow exception, which is one of several possible
However, this can be recovered, as smaller values (subnormal numbers)
can be represented in denormalized format. This requires various
tricks as the leading digits of the mantissa can now be $0$ rather
than an implicit $1$. Skipping the details, what this amounts to
is that underflow can be overcome, to some extent, by using subnormal
numbers that have less precision than the normal ones.
Thus if the computation has provision for using subnormal numbers, it
is less likely to be aborted by an underflow. But then one should
watch for the precision which may not be as good as normally expected.