# Information, Signals, and the Physics of Computing

Computer Science I · Physics · https://tryals.app/learn/computer-science-i/information-signals-and-the-physics-of-computing

## Computation Is Physical

Computation is a physical process. Every bit stored, gate switched, and message sent obeys physics, which both **enables** and **limits** computing.

**Signals carry information physically.** A bit is represented by a physical quantity: voltage, charge, light pulses, or magnetic orientation. Real signals are **analog** (continuous) but interpreted **digitally** via **thresholding**.

| Signal Type | Nature | Function |
| --- | --- | --- |
| **Analog** | Continuous | Physical world representation |
| **Digital** | Thresholded | Offers **noise immunity** |

Small disturbances do not flip bits, ensuring reliability.

## Physics Limits & Enables

Physics sets hard limits on computing performance. Switching transistors takes **energy** and produces **heat** ($P = I^2R$), bounding chip speeds. The **speed of light** limits signal transit across chips, and thermodynamics sets an energy floor for bit erasure.

| Physical Limit | Consequence |
| --- | --- |
| **Heat** ($P = I^2R$) | Clock speeds plateaued; chips went parallel |
| **Speed of Light** | Bounds critical path clock speeds |

> **Common pitfall:** Treating computation as purely abstract. Every bit is **embodied** physically, and every operation costs energy and time bounded by law.

## Practice questions

7 of this lesson's 13 practice questions, with answers. The full set is in the app.

### 1. An analog-to-digital converter uses 8 bits per sample. How many distinct levels can it distinguish?

**Answer:** 256

**Why:** 2 to the power 8 is 256. Answering 8 confuses the number of bits with the number of levels; adding a single bit doubles the resolution, which is why converter bit-depths are quoted rather than level counts.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/an-analog-to-digital-converter-uses-8-bits-per-sample-how-many

### 2. A digital receiver reads any voltage above 2.5 volts as a 1 and anything below it as a 0. Sort each measured voltage by the bit it is interpreted as.

**Answer:**

- Read as 1: 3.1 volts, 4.8 volts, 2.6 volts
- Read as 0: 0.4 volts, 2.4 volts

**Why:** Only the side of the threshold matters, so 2.4 and 2.6 volts are read as opposite bits despite differing by a fifth of a volt. Signals near the threshold are exactly where noise causes errors, which is why real designs keep the levels far from it.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/a-digital-receiver-reads-any-voltage-above-2-5-volts-as-a-1-and

### 3. A current of 3 amperes flows through a component of resistance 2 ohms. How much power is dissipated as heat, in watts?

**Answer:** 18

**Why:** 9 times 2 = 18 W. The current is squared, so doubling it would quadruple the heat, the reason a chip's power budget, not its logic, is what caps how fast it can be clocked.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/a-current-of-3-amperes-flows-through-a-component-of-resistance-2

### 4. Select every genuine physical limit on computing that the lesson identifies.

A. Digital signals are restored to clean levels at each stage, so noise does not accumulate.
B. Analogue signals can be copied indefinitely without degradation.
C. Every bit is stored in some physical state - a charge, a magnetisation, a pit.
D. Erasing information has an unavoidable energy price, however good the hardware becomes.
E. A noise margin is the voltage range treated as a valid logic level.

**Answer:** A. Digital signals are restored to clean levels at each stage, so noise does not accumulate.; B. Analogue signals can be copied indefinitely without degradation.; C. Every bit is stored in some physical state - a charge, a magnetisation, a pit.; D. Erasing information has an unavoidable energy price, however good the hardware becomes.

**Why:** Heat removal, signal propagation, Landauer's erasure floor and physical embodiment are all consequences of physical law. The count of possible algorithms is a mathematical matter and no physical constraint touches it.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/select-every-genuine-physical-limit-on-computing-that-the-lesson

### 5. Landauer's principle sets a minimum energy for **erasing** a bit and none for computing with one. Why is erasure the operation that costs?

A. Because erasure is logically irreversible, so entropy must be paid
B. Because erasure takes longer than other operations
C. Because writing a zero requires more energy than writing a one
D. Because erased bits must be physically overwritten several times

**Answer:** A. Because erasure is logically irreversible, so entropy must be paid

**Why:** Two states collapsing to one lowers the memory's entropy, and the second law requires an equal increase elsewhere, kT ln 2 per bit, released as heat. Reversible operations destroy no information and carry no such floor, which is the basis of reversible computing and why quantum gates are unitary.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/landauers-principle-sets-a-minimum-energy-for-erasing-a-bit-and-none

### 6. Complete the reason digital systems are so reliable.

**Answer:** Digital systems tolerate noise because **a small analog disturbance does not push the signal across the threshold**.

**Why:** Because the receiver only asks which side of the threshold the voltage is on, small wobbles are discarded entirely. The wires do carry genuine analog voltages, and this thresholding is what turns them into clean, restorable bits.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/complete-the-reason-digital-systems-are-so-reliable

### 7. A reversible circuit computes its result, then runs the same steps backwards to restore the inputs, keeping only a copy of the answer. What does Landauer's principle say about the energy this costs?

A. Nothing, the principle applies only to clearing a whole register, not to individual bits.
B. In principle it can approach zero, because nothing is erased.
C. Unchanged, because the energy floor is set by the number of operations performed.
D. Exactly double, because every logic step is performed twice.

**Answer:** B. In principle it can approach zero, because nothing is erased.

**Why:** The bound is on destroying information, not on computing, so the cost is per bit ERASED rather than per gate. Uncomputing returns the scratch bits instead of discarding them; only the copied answer cannot be returned.

Page: https://tryals.app/practice/computer-science-i/information-signals-and-the-physics-of-computing/a-reversible-circuit-computes-its-result-then-runs-the-same-steps