Why computers do not use ten states

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

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

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'

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

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

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

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1voltage < 2.5 → 0		Anoise = 0.3 V, signal 4.7 V → 1
2levels = 10, gap = 0.5 V		Blevel 6 = 3.0 V + noise 0.5 V → level 7
3Electrical noise can nudge a signal up or down, but a two-state system still reads it correctly if the nudge is small.		CA 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.
4With ten states, a small amount of noise can push a signal into the next level and cause an error.		DComputers can make many voltages. Binary is used because two states are reliable and cheap, not because other voltages are impossible.
5Ten states are better because they are harder to confuse than two.		ETen voltage levels squeezed into 5 volts leave only a tiny gap between each level, so they are easy to confuse.
6Binary is used because computers cannot make any voltage except 0 V.		FThis is backwards. Ten states are closer together, so they are easier to confuse than two states.

Definitions

binary reliability

Fill in the Blanks

Complete each line of code by filling in the missing parts.

binaryStates ← _ decimalLevels ← 10

IF noise _ margin THEN error ← TRUE

IF voltage _ 2.5 THEN bit ← 0 ELSE bit ← 1

weakSignal ← 2.9 IF weakSignal > 2.5 THEN bit ← _

IF voltage > 2.5 THEN bit ← 1 ____ bit ← 0

Spot the Error

Shade in the letter of the line that contains an error.

Question 1

A volts = 4.8

B if volts > 2.5

C print("on")

D else:

E print("off")

Question 2

A states = 2

B noise = 0.3

C gap = 5 / (states - 1)

D if noise < gap / 2

E print("reliable")

Question 3

A levels = "10"

B gap = 5 / (levels - 1)

C print(gap)

D print("tiny gap")

Question 4

A signal = 5.0

B noise == 0.8

C received = signal - noise

D print(received)

Question 5

A def read_bit(volts):

B if volts >= 2.5:

C return one

D return 0

Answer Key

Why computers do not use ten states

Section A: Quick Questions

A — Two states are easier to tell apart, so errors are less likely

B — Two states: a weak 'on' is still clearly not 'off'

A — Unwanted small changes in a signal that can nudge its voltage up or down

A — A level 4 signal could be misread as a level 5

B — They can be built cheaply because they only need to detect on or off

Section B: 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.

Section C: Definitions

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.

Section D: Fill in the Blanks

binaryStates ← 2
decimalLevels ← 10

IF noise > margin THEN
  error ← TRUE

IF voltage < 2.5 THEN bit ← 0
ELSE bit ← 1

weakSignal ← 2.9
IF weakSignal > 2.5 THEN bit ← 1

IF voltage > 2.5 THEN bit ← 1
ELSE bit ← 0

Section E: Spot the Error

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:

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:

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

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

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