Figure $7$ shows the algorithmic state diagram for a coffee machine. This coffee machine can be used to dispense either an espresso coffee or a latte depending on a user's selection, which is made in the state $00.$

In both states $01($dispense milk state$)$ and $11($dispense coffee state$)$ a binary counter is used to time the milk or coffee dispense action.

Assuming the binary counter is the same one discussed in Lectorial $10($the $74$LS$193),$ select from the options below what the Clear output should be set to in each of the four states $(00,01,10$ and $11).$

is the proportion of Carbon $14$ in the organism $($initially this is considered to be $1$ upon the moment of death$)$ and

is the rate of decay, which is a constant

giving a half$-$life of Carbon $14$ of approx. $5730$ years.

This system is to be modelled using Simulink, this is shown in Figure $5$:

Carbon$14\_$Model.JPG

Figure $5$: A Simulink model of Radiocarbon Dating

From the options below, give the appropriate value of the Initial condition that should be entered into the Integrator block.

Assume the Simulation time$-$step is set to $1$ year increments.

Group of answer choices

Initial Condition $=1$

Initial Condition $=-5730$

Initial Condition $=-1\mathrm{.}21$e$-4$

Initial Condition $=0$

Initial Condition $=+1\mathrm{.}21$e$-4$

Initial Condition $=5730$