Consider an Ethernet segment with a transmission speed of $10^8$ bits/sec and a maximum segment length of 500 meters. If the speed of propagation of the signal in the medium is $2\times 10^8$ meters/sec, then the minimum frame size ($\textit{in bits}$) required for collision detection is ________

In CSMA/CD Ethernet, the condition for collision detection is that the transmission time ($T_t$) must be at least twice the propagation delay ($T_p$):

1. Propagation Delay ($T_p$):

   $$T_p = \frac{\text{Length}}{\text{Propagation Speed}} = \frac{500\text{ m}}{2 \times 10^8\text{ m/s}} = 2.5 \times 10^{-6}\text{ s}$$

2. Minimum Frame Size ($L_{\min}$):

   $$\frac{L_{\min}}{\text{Bandwidth}} \ge 2 \times T_p$$

   $$L_{\min} = 2 \times T_p \times B = 2 \times (2.5 \times 10^{-6}\text{ s}) \times 10^8\text{ bits/s} = 500\text{ bits}$$

Thus, the minimum frame size required is 500 bits.