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REVISION AND PRACTICE

Week 1 — Quick Revision

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Start here Week 1 on one page: from “what is a computer” to bits and binary numbers.

Problem → layers → transistors → voltages → 0 and 1 → binary numbers → logic.
Problem → layers → transistors → voltages → 0 and 1 → binary numbers → logic.
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Week 1 at a glance

Big ideas

  • Every computer computes, remembers and communicates.
  • A problem reaches hardware through layers: problem → algorithm → program → system software → instruction set → microarchitecture → logic → circuits → electrons. This course: logic up to a simple CPU.
  • Chips are built in levels (transistor → gate → module → chip → board → device) using abstraction.
  • Moore’s Law: transistors per chip double about every 2 years (1965 paper said every year; revised in 1975).
  • Information is stored as voltage (e.g. 0 V black, 1 V white).
  • Noise piles up in analog chains. The digital abstraction reads only low/high, so each block restores a clean signal.
  • V ≤ V_L → 0, V ≥ V_H → 1, between = forbidden zone.
  • Binary = 2 values. n bits → 2ⁿ values. Binary place values: 1, 2, 4, 8, 16…
  • Other bases: hex digit = 4 bits (A–F=10F = 1 0–15); any base → decimal by place values; unknown bases: test the options in the equation.
  • Boole (1854): logic as maths. Shannon (1937): logic with switches (series = AND, parallel = OR).

Formulas and methods

Task Method
Values from n bits 2ⁿ (largest number 2ⁿ − 1)
Bits for N things smallest n with 2n≥N2^{n} \ge N
Binary → decimal add place values where the bit is 1
Decimal → binary divide by 2 repeatedly, read remainders bottom to top
Read a voltage compare with V_L and V_H
Moore’s Law T/F Y ÷ X=2n→X = 2^{n} \to time = 2n years
Binary ↔︎ hex groups of 4 bits from the right
Bits to write number N 2n−1≤N2^{n-1} \le N < 2ⁿ

Practice questions

  1. What are the three building blocks of a computing system?
Computing unit, memory/storage unit, communication unit.
  1. Put in order, top to bottom: logic, algorithm, program, electrons, instruction set.
Algorithm → program → instruction set → logic → electrons.
  1. A chip had 1 million transistors. Following Moore’s Law (2 years), about how many after 6 years?
2³ = 8 → about 8 million.
  1. V_L = 0.5 V, V_H = 2.5 V. Read 0.4 V, 1.2 V, 2.8 V.
0, forbidden, 1.
  1. Why does a digital chain not pile up noise?
Each block reads only low/high and outputs a clean 0 or 1, removing small errors.
  1. How many bits to number 1,000 items?
2¹⁰ = 1024 ≥ 1000 → 10 bits.
  1. Convert 10110₂ to decimal and 37 to binary.
16 + 4 + 2 = 22; 37 = 32 + 4 + 1 = 100101₂.
  1. Switches in parallel act like which gate?
OR.
  1. True or false: 2 million transistors today → about 32 million in 8 years (Moore’s Law).
True: 16× = 2⁴ = 4 doublings × 2 years = 8 years.
  1. (431)₆ in hex?
4×36 + 3×6 + 1 = 163 = 0xA3.
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