1. The message consists of 280 characters. Show that the total amount of digital data in this message is 2240 bits.
2. The transmitter sends this digital data at a rate of $14{kB\; s}^{-1}$ (where $1kB=1000bytes$). Determine the minimum time required to send a 280-character message.

1. Describe one origin of electrical noise in a communication system.
2. Describe the effect that electrical noise can have on the signal and on the communication system.

A noisy digital signal is applied to a Schmitt trigger circuit. The circuit output $V_{out}$ switches to:

• $12V$ when the input voltage $V_{in}$ falls below $2.0V$
• $0V$ when the input voltage $V_{in}$ rises above $4.0V$

The input voltage $V_{in}$ over a $10\mu s$ interval is described by four stages:

• For $t\in [0,2]\mu s$: $V_{in}$ increases linearly from $1.0V$ to $5.0V$
• For $t\in [2,6]\mu s$: $V_{in}$ decreases linearly from $5.0V$ to $1.0V$
• For $t\in [6,8]\mu s$: $V_{in}$ increases linearly from $1.0V$ to $5.0V$
• For $t\in [8,10]\mu s$: $V_{in}$ decreases linearly from $5.0V$ to $3.0V$

Assuming that $V_{out}$ is initially at $12V$ at $t=0$, determine the exact times $t$ at which $V_{out}$ transitions, and state the final value of $V_{out}$ at $t=10\mu s$.