Depending on how that boolean changes you could expose it as an Observable<boolean> on your service, and then subscribe to that stream in your component. Your service would look something like:

@Injectable()
export class MyBooleanService {
    myBool$: Observable<boolean>;

    private boolSubject: Subject<boolean>;

    constructor() {
        this.boolSubject = new Subject<boolean>();
        this.myBool$ = this.boolSubject.asObservable();
    }

    ...some code that emits new values using this.boolSubject...
}

Then in your component you would have something like this:

@Component({...})
export class MyComponent {
    currentBool: boolean;

    constructor(service: MyBooleanService) {
        service.myBool$.subscribe((newBool: boolean) => { this.currentBool = newBool; });
    }
}

Now depending on what you need to do with that bool value you may need to do some other things to get your component to update, but this is the gist of using an observable. Note, you will want to unsubscribe from the myBool$ stream at some point to prevent memory leaks and unexpected side effects.

Another option is you use the async pipe within your template instead of explicitly subscribing to the stream in the constructor. That will also ensure the subscription is disposed of automatically. Again though, that depends on what exactly you need to do with the bool values.

The Sam's answer is completely right. I would just want to add that you could also leverage a TypeScript setter to automatically trigger the event for changes:

@Injectable()
export class MyBooleanService {
    myBool$: Observable<boolean>;

    private boolSubject: Subject<boolean>;
    private _myBool: Boolean;

    constructor() {
        this.boolSubject = new Subject<boolean>();
        this.myBool$ = this.boolSubject.asObservable();
    }

    set myBool(newValue) {
      this._myBool = newValue;
      this.boolSubject.next(newValue);
    }
}