← ACARA Digital Technologies Years 7–8

The two-state (on/off) system

A system with only two possible conditions, like a light switch being off or on. We write the two states as 0 and 1, which is the idea behind binary.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 1

Understanding The two-state (on/off) system in ACARA Digital Technologies Years 7–8

What it does: Reading each switch left to right as 0 for off and 1 for on gives the binary pattern 011. Each bead has only two possible colours, so the bracelet is a two-state system that spells out 101. The two states are written as 0 and 1. Binary uses only these two digits. We usually write off as 0 and on as 1. Read each light in order: on = 1, off = 0, on = 1, on = 1. So the pattern is 1011. A switch is either off (0) or on (1), which makes it a simple two-state system.

Common mistakes: A two-state system only has the values 0 and 1. Off is written as 0, so the line should be state = 0, not 2. The value 1 means on. When switch == 1 the program should print "light is on", not "light is off".

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This module's key terms are also in a printable crossword (Modules 173–188) and word search (Modules 153–188).

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Learning
Duo
A light switch is either off or on. Is this a two-state system?
Yes, it has only two possible conditionsNo, it needs ten conditions to count
Matches
A light switch has 3 states: 0, 1, 2
↓
A light switch only has two states, off and on, so it uses only 0 and 1. There is no state 2.
Applying
Meanings
Term
two-state system
Meaning
A system with only two possible conditions, like a light switch being off or on. We write the two states as 0 and 1, which is the idea behind binary.
Practice
light ← 0
Testing
Gaps
light ← // the light is off
Check Answer
Spots
1light = "off"
2state = 2

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Quick Questions

1. A light switch is either off or on. Is this a two-state system?
A. Yes, it has only two possible conditions ✓
B. No, it needs ten conditions to count
A light switch can only be off or on, so it is a two-state system.
2. In binary, which pair of digits is used to write the two states?
A. 0 and 1 ✓
B. 1 and 2
The two states are written as 0 and 1. Binary uses only these two digits.
3. A light switch is off. Which digit shows this state?
A. 1
B. 0 ✓
We usually write off as 0 and on as 1.
4. A row of 4 lights is on, off, on, on. How is this written in binary?
A. 1101
B. 1011 ✓
Read each light in order: on = 1, off = 0, on = 1, on = 1. So the pattern is 1011.
5. Which of these is NOT a two-state system?
A. A dimmer dial with 10 brightness levels ✓
B. A door that is open or closed
A dimmer has many levels, so it is not two-state. A door that is open or closed has only two conditions.

Match the Pairs

off = 0, on = 1 → A two-state system written in binary: off is 0 and on is 1.
light switch: 0 or 1 → A light switch has only two states, so it can be shown with one binary digit.
Three light switches in a row can show a binary pattern, where off is 0 and on is 1. → off on on = 011
A binary bracelet uses two bead colours: one colour means 0 and the other means 1. → white = 0, black = 1: black white black = 101
A light switch has 3 states: 0, 1, 2 → A light switch only has two states, off and on, so it uses only 0 and 1. There is no state 2.
off = 1, on = 0 (in the usual binary rule) → The usual rule is the other way round: off is 0 and on is 1.

Key Term

two-state system
A system with only two possible conditions, like a light switch being off or on. We write the two states as 0 and 1, which is the idea behind binary.

Fill in the Blanks

1. light ← 0 // the light is off
Hint: Type the digit we use to show the off state.
2. bead ← 1 // the bead is on
Hint: Type the digit we use to show the on state.
3. IF switch = 1 THEN DISPLAY "Light is on" END IF
Hint: Type the digit that means the switch is on.
4. states ← 2 // off and on
Hint: Type how many possible conditions a two-state system has.
5. switch ← NOT switch // flip the state
Hint: Type the keyword that flips a state to its opposite.

Spot the Error

Question 1
A light = "off"
B state = 2
C if light == "on":
D state = 1
E print(state)
Line B — A two-state system only has the values 0 and 1. Off is written as 0, so the line should be state = 0, not 2.
Question 2
A switch = 1
B if switch == 1:
C print("light is off")
D else:
E print("light is off")
Line C — The value 1 means on. When switch == 1 the program should print "light is on", not "light is off".
Question 3
A states = ["off", "on"]
B switch = 1
C print(states[2])
Line C — A two-state list only has positions 0 (off) and 1 (on). Position 2 does not exist. It should be states[switch] or states[1].
Question 4
A light = "on"
B if light = "on":
C bit = 1
D else:
E bit = 0
Line B — A single = assigns a value. To check whether the light is on, use the comparison ==, so the line should be if light == "on":.
Question 5
A states = ["off", "on", "dim"]
B print(len(states))
C # output: 2
Line A — A two-state system has only two conditions. Adding "dim" makes three states, so the list should be just ["off", "on"].

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