A real number

$x$ between 0 and 1 is called normal to the base

$b$, an integer

$>1$, if the digits in the

${b}^{n}$-ary expansion of

$x$ are asymptotically uniformly distributed for every fixed positive integer

$n$. If

$x$ is normal to every base

$b$, then

$x$ is called absolutely normal. On the other hand, a number

$x$ is abnormal to the base

$b$ if

$x$ is not normal, and

$x$ is absolutely abnormal, if it is abnormal to every base. While it is easy to construct absolutely normal numbers, it is far more difficult to find numbers which are absolutely abnormal. A reason for the second claim is partially due to the fact that, with respect to Lebesgue measure, almost all numbers are absolutely normal. The author constructs absolutely abnormal numbers and then shows that the constructed number has the required property.