diff --git a/calc.html b/calc.html
index d82ff41b8a1c85ebced6059fe2a704bc35596382..63da207c4666d31948e1673055b28c80a31f5f8a 100644
--- a/calc.html
+++ b/calc.html
@@ -109,6 +109,7 @@
       </div>
     </div>
     <script type="text/javascript" src="vendor/jquery.min.js"></script>
+    <script type="text/javascript" src="fsm.js"></script>
     <script type="text/javascript">
       (function () {
 	  /**
@@ -129,6 +130,16 @@
 
 	  // page init
 	  showDumbData();
+	  console.assert(fsm.matchesSubstringAbb("123abb123") === true);
+	  console.assert(fsm.matchesSubstringAbb("123ab123") === true);
+	  console.assert(fsm.matchesSubstringAbb("123abaabb123") === true);
+	  console.assert(fsm.matchesSubstringAbb("123abbb123") === true);
+	  console.assert(fsm.matchesSubstringAbb("123ababab123") === false);
+	  console.assert(fsm.matchesSubstringAbb("") === false);
+	  console.assert(fsm.matchesSubstringAbb("123") === false);
+	  console.assert(fsm.matchesSubstringAbb("123ab") === false);
+	  console.assert(fsm.matchesSubstringAbb("123abb") === true);
+	  console.assert(fsm.matchesSubstringAbb("abb") === true);
 
 	  // setup event handler
 	  $('.keyboard td').click(function (evt) {
diff --git a/fsm.js b/fsm.js
new file mode 100644
index 0000000000000000000000000000000000000000..c51fb0320a82f08c36854ccf250026c7dd6b5f18
--- /dev/null
+++ b/fsm.js
@@ -0,0 +1,76 @@
+var fsm = function () {
+    const debugging = false;
+
+    const debug = function (msg) {
+	if (debugging) {
+	    console.log(msg);
+	}
+    };
+
+    /**
+     * a fsm that tries to match string "abb". see function
+     * matchesSubstringAbb.
+     */
+    const matchAbbMachine = function () {
+	this.stateWaitForA = "wait for a";
+	this.stateWaitForFirstB = "wait for 1st b";
+	this.stateWaitForSecondB = "wait for 2nd b";
+	this.stateSucceed = "succeed";
+
+	this.currentState = "wait for a";
+	this.readch = function (ch) {
+	    switch (this.currentState) {
+	    case this.stateWaitForA:
+		if (ch === 'a') {
+		    this.currentState = this.stateWaitForFirstB;
+		} else {
+		    this.currentState = this.stateWaitForA;
+		}
+		break;
+	    case this.stateWaitForFirstB:
+		if (ch === 'b') {
+		    this.currentState = this.stateWaitForSecondB;
+		} else if (ch === 'a') {
+		    // do nothing, keep current state.
+		} else {
+		    this.currentState = this.stateWaitForA;
+		}
+		break;
+	    case this.stateWaitForSecondB:
+		if (ch === 'b') {
+		    this.currentState = this.stateSucceed;
+		} else if (ch === 'a') {
+		    this.currentState = this.stateWaitForFirstB;
+		} else {
+		    this.currentState = this.stateWaitForA;
+		}
+		break;
+	    case this.succeed:
+		// do nothing, keep current state.
+		break;
+	    }
+	    debug("readch " + ch + ", currentState is " + this.currentState);
+	    return this.currentState;
+	};
+    };
+
+    /**
+     * return true if given string has substring "abb" in it.
+     * implemented using fsm.
+     */
+    const matchesSubstringAbb = function (str) {
+	var machine = new matchAbbMachine();
+	for (i = 0; i < str.length; ++i) {
+	    machine.readch(str[i]);
+	    if (machine.currentState === "succeed") {
+		// console.log("matches");
+		return true;
+	    }
+	}
+	return false;
+    };
+
+    return {
+	matchesSubstringAbb: matchesSubstringAbb
+    };
+}();
diff --git a/operational b/operational
index bfecf1181b3b5880a2487f80552475098331f35f..e192246c8c115e1b003831e9b4277e84ec1139f9 100644
--- a/operational
+++ b/operational
@@ -15,6 +15,36 @@ the parent DOM.
 
 * current                                                             :entry:
 ** 
+** 2017-01-26 design data structure for the calculator.
+- this can be written and tested independently from the web UI.
+- basic data:
+  - stack of numbers.
+  - current state and data in finite state machine (fsm).
+  - data for undo. I think I can just take a snapshot of the fsm.
+
+- how many states are there?
+
+  init state is "waiting for number".
+
+  | this state                   | event                     | next state                                       |
+  |------------------------------+---------------------------+--------------------------------------------------|
+  | waiting                      | press num keys or dot key | modify number, then waiting for number or action |
+  | waiting for number or action | press num keys or dot key | modify number, then waiting for number or action |
+  | waiting for number or action | press return key          | commit number, then waiting                      |
+  | waiting for number or action | press +-*/                | commit number, do op, then waiting               |
+  | waiting for number or action | press < key               | modify number, then waiting for number or action |
+
+  There is no "ending state", the machine can always accept new keyboard events.
+
+- a few display and error handling.
+
+  - when number is "0", press more num0 will just show error and not modify the number.
+
+  - when number is "", press dot will change number to "0."
+
+  - when number already has a dot in it, future dot will just show error and
+    not modify the number.
+
 ** 2017-01-26 make basic number input and arithmetic work
 - DONE make event work.
   - TODO add some visual feedback when clicking a button. like in material design.
@@ -37,5 +67,20 @@ trail cache. it's not a problem.
 - make DUP and SWP work
 - make trail work
 * done                                                                :entry:
+** 2017-01-26 how to write a fsm simulator in javascript.
+- try write an easier example before writing the real thing.
+- easy example:
+  check whether a string has substring "abb".
+
+  states:
+  | this state       | event                 | next state                                                                                    |
+  |------------------+-----------------------+-----------------------------------------------------------------------------------------------|
+  | wait for "a"     | read new character ch | if ch is "a", wait for 1st "b"; otherwise, wait for "a"                                       |
+  | wait for 1st "b" | read new character ch | if ch is "b" => wait for 2nd "b"; if ch is "a" => wait for 1st "b"; otherwise => wait for "a" |
+  | wait for 2nd "b" | read new character ch | if ch is "b" => succeed; if ch is "a" => wait for 1st "b"; otherwise => wait for "a"          |
+  | succeed          | ∅                     | ∅                                                                                             |
+
+- it works.
+
 ** 2017-01-26 draw the keyboard using HTML and CSS
 * wontfix                                                             :entry: