← ACARA Digital Technologies Years 7–8

Why computers do not use ten states

Two states (on or off) are easy to tell apart even when signals are weak or noisy. Ten voltage levels would be easy to confuse, so binary makes errors less likely.

Part of: ACARA Digital Technologies Years 7–8 — Binary Number Representation — Module 27

Understanding Why computers do not use ten states in ACARA Digital Technologies Years 7–8

What it does: Even with 0.3 V of noise, 4.7 V is still clearly high, so it is read as 1 and no error happens. Levels are only 0.5 V apart, so 0.5 V of noise makes level 6 look like level 7, which gives a wrong value. Telling 'on' from 'off' is easy. Telling ten close voltage levels apart is much harder, so binary is more reliable. Circuits that only decide between two states are simple. Circuits that measure many precise levels would be more complex and costly. The computer only has to decide high or low. It does not need an exact measurement, which keeps it reliable.

Common mistakes: An if line must end with a colon. With only two states, one threshold check is enough to tell on from off. It should be: if volts > 2.5:. An if line must end with a colon. With two states the gap is big (5), so noise is much smaller than half the gap and the signal is reliable. It should be: if noise < gap / 2:.

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This module's key terms are also in a printable crossword (Modules 189–203) and word search (Modules 189–236).

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Learning
Duo
Why do computers use only two states (on and off) instead of ten voltage levels?
Ten states would make the computer too smart to controlTwo states are easier to tell apart, so errors are less likely
Matches
Ten states are better because they are harder to confuse than two.
↓
This is backwards. Ten states are closer together, so they are easier to confuse than two states.
Applying
Meanings
Term
binary reliability
Meaning
Two states (on or off) are easy to tell apart even when signals are weak or noisy. Ten voltage levels would be easy to confuse, so binary makes errors less likely.
Practice
signal ← 4.6
Testing
Gaps
binaryStates ←
Check Answer
Spots
1volts = 4.8
2if volts > 2.5

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Quick Questions

1. Why do computers use only two states (on and off) instead of ten voltage levels?
A. Two states are easier to tell apart, so errors are less likely ✓
B. Ten states would make the computer too smart to control
Telling 'on' from 'off' is easy. Telling ten close voltage levels apart is much harder, so binary is more reliable.
2. A signal gets a little weak on its way along a wire. Which system copes better?
A. Ten states: a weak signal is still easy to match to the right level
B. Two states: a weak 'on' is still clearly not 'off' ✓
With only two states there is a big gap between them. With ten levels, a small drop could look like the next level down.
3. What is electrical noise?
A. Unwanted small changes in a signal that can nudge its voltage up or down ✓
B. The sound a computer makes when it turns on
Noise is random interference on a wire. It slightly changes the voltage and can cause mistakes if levels are too close together.
4. Imagine ten voltage levels, each only a small step apart. What could noise cause?
A. A level 4 signal could be misread as a level 5 ✓
B. Nothing, because more levels always means more accuracy
When levels are close together, a small bump from noise can push the voltage into the wrong level and the computer reads the wrong digit.
5. Which statement about binary circuits is true?
A. They are expensive because they must measure ten exact voltages
B. They can be built cheaply because they only need to detect on or off ✓
Circuits that only decide between two states are simple. Circuits that measure many precise levels would be more complex and costly.

Match the Pairs

voltage < 2.5 → 0 → A simple rule for a two-state system: any signal below the halfway point is read as 0 (off), so a small wobble rarely changes the answer.
levels = 10, gap = 0.5 V → Ten voltage levels squeezed into 5 volts leave only a tiny gap between each level, so they are easy to confuse.
Electrical noise can nudge a signal up or down, but a two-state system still reads it correctly if the nudge is small. → noise = 0.3 V, signal 4.7 V → 1
With ten states, a small amount of noise can push a signal into the next level and cause an error. → level 6 = 3.0 V + noise 0.5 V → level 7
Ten states are better because they are harder to confuse than two. → This is backwards. Ten states are closer together, so they are easier to confuse than two states.
Binary is used because computers cannot make any voltage except 0 V. → Computers can make many voltages. Binary is used because two states are reliable and cheap, not because other voltages are impossible.

Key Term

binary reliability
Two states (on or off) are easy to tell apart even when signals are weak or noisy. Ten voltage levels would be easy to confuse, so binary makes errors less likely.

Fill in the Blanks

1. binaryStates ← 2 decimalLevels ← 10
Hint: Type the number of states a binary signal uses (on or off).
2. IF noise > margin THEN error ← TRUE
Hint: Type the comparison operator for 'is greater than'. Noise bigger than the safe gap causes a mistake.
3. IF voltage < 2.5 THEN bit ← 0 ELSE bit ← 1
Hint: Type the comparison operator for 'is less than'. A low voltage reads as off.
4. weakSignal ← 2.9 IF weakSignal > 2.5 THEN bit ← 1
Hint: Type the bit value that a weak but still high signal is read as.
5. IF voltage > 2.5 THEN bit ← 1 ELSE bit ← 0
Hint: Type the keyword for the other case, so only two outcomes are possible.

Spot the Error

Question 1
A volts = 4.8
B if volts > 2.5
C print("on")
D else:
E print("off")
Line B — An if line must end with a colon. With only two states, one threshold check is enough to tell on from off. It should be: if volts > 2.5:
Question 2
A states = 2
B noise = 0.3
C gap = 5 / (states - 1)
D if noise < gap / 2
E print("reliable")
Line D — An if line must end with a colon. With two states the gap is big (5), so noise is much smaller than half the gap and the signal is reliable. It should be: if noise < gap / 2:
Question 3
A levels = "10"
B gap = 5 / (levels - 1)
C print(gap)
D print("tiny gap")
Line A — The number of levels is in quotes, so it is text. Text cannot be used in levels - 1, so the program crashes. It should be: levels = 10
Question 4
A signal = 5.0
B noise == 0.8
C received = signal - noise
D print(received)
Line B — Two equals signs compare values instead of storing one, so noise is never created and the next line fails. It should be: noise = 0.8
Question 5
A def read_bit(volts):
B if volts >= 2.5:
C return one
D return 0
Line C — one is not a number and no variable called one exists, so the program crashes. A bit read as on must return the number 1. It should be: return 1

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