Answer
$01001001$ $(\frac{9}{16})$ is larger than $00111101$ $(\frac{13}{32})$.
Work Step by Step
$01001001$ $(\frac{9}{16})$ is larger than $00111101$ $(\frac{13}{32})$. The following is a simple way of determining which of two patterns represents the larger value:
$Case\ 1$. If the sign bits are different, the larger is the one with 0 sign bit.
$Case\ 2$. If the sign bits are both $(0)$, scan the remaining portions of the patterns from left to right until a bit position is found where the two patterns differ. The pattern containing the $(1)$ in this position represents the larger value.
$Case\ 3$. If the sign bits are both $(1)$, scan the remaining portions of the patterns from left to right until a bit position is found where the two patterns differ. The pattern containing the $(0)$ in this position represents the larger value. The simplicity of this comparison process is one of the reasons for representing the exponent in floating-point systems with an excess notation rather than with two’s complement.
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also, see image below:
