Base CS from zero
What a computer is: multiple-choice review
Crux Multiple-choice synthesis across the unit: why two states win, place value, encodings, boolean completeness, and gates building arithmetic.
Your altitude — climbing toward senior
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You are at middle altitude — in the skySix questions that span the whole unit — from why a transistor has two states, up to how those same two states become numbers, letters, colours, truth values, and finally arithmetic. Each one asks you to connect two ideas, not recite one definition.
Goal
Confirm you can trace the single thread that runs through the unit: two-state hardware to bits to place value to encodings to boolean logic to gates to arithmetic. If the connections hold, the unit’s mental model is solid.
Quiz
Completed
A junior engineer asks why chips do not use ten voltage levels (one per decimal digit) to pack more into each wire. What is the real reason hardware settled on two?
Heads-up Speed is not the reason; hardware could be built for decimal (ENIAC was). The decisive factor is reliability — a wide noise margin between just two levels.
Heads-up Decimal has been used for millennia, and early machines were decimal. Binary was a deliberate engineering choice for noise immunity, not a historical accident.
Heads-up Power is not the driver. The point is the size of the gap relative to noise: two levels maximise that margin, so reads stay reliable.
Quiz
Completed
A colleague says 'a 16-bit number can hold twice as much as an 8-bit number.' Why is this wrong, and what is the right statement?
Heads-up Adding bits multiplies the count, it does not add or double linearly. Going from 8 to 16 bits multiplies the range by 2⁸ = 256, not by 2.
Heads-up Each extra bit multiplies by 2, not by adding a factor of 1. Eight extra bits means 2⁸ = 256x, not 16x.
Heads-up Sign is a separate interpretation choice. For unsigned ranges, 16 bits holds 65,536 values — 256x the 8-bit range, regardless of sign.
Quiz
Completed
A teammate insists the byte 01000001 'is the letter A.' Correct the statement at the level this unit teaches.
Heads-up Nothing about the bits forces the letter reading. The same byte is 65 as a number or a colour channel; only the chosen encoding fixes the meaning.
Heads-up 65 is no more 'true' than 'A'. Both are valid interpretations under different encodings. Neither is privileged; the bits carry no meaning by themselves.
Heads-up The point is deeper than UTF-8 vs UTF-16: a numeric reader or an image reader sees the same byte as a number or a colour. The encoding agreement, not just the text encoding, decides the meaning.
Quiz
Completed
Why is a truth table called the definition of a boolean operation, rather than just a summary of it?
Heads-up A truth table says nothing about implementation or speed; it only specifies input-to-output behaviour. That behaviour is the whole definition.
Heads-up Boolean inputs are exhaustively 0 or 1, so the table covers every case exactly — no approximation. That completeness is precisely why it counts as the definition.
Heads-up Precedence is a separate parsing rule for expressions. A single operation's truth table just maps its own inputs to outputs — that mapping defines it.
Quiz
Completed
Someone claims XOR must be a hardware primitive because 'if statements need it.' Using what the unit teaches about completeness, how do you respond?
Heads-up XOR is built directly from AND, OR, NOT. Those three are functionally complete, so no extra primitive is required for XOR or any other boolean function.
Heads-up Having a distinct truth table does not require a distinct primitive. Disjunctive normal form builds any truth table from AND, OR, NOT alone.
Heads-up It is the opposite — NOT is essential to the construction (to negate inputs per row). With AND, OR, NOT together, every boolean function including XOR is expressible.
Quiz
Completed
In a half-adder summing two bits, why is the sum bit wired from an XOR circuit and the carry bit from an AND gate?
Heads-up AND is 1 only when both inputs are 1, which matches the carry, not the sum. The sum is 1 when inputs differ — that is XOR, not AND.
Heads-up For inputs 1 and 1, OR gives 1, but the correct sum bit is 0 (with carry 1). OR cannot produce the sum; XOR (true only when inputs differ) does.
Heads-up Sum and carry are different functions of the same inputs, so they need different gates wired in parallel — XOR for sum, AND for carry — not one gate read twice.
Recap
The unit is one chain: two-state hardware exists because a wide noise gap makes reads reliable; bits grouped by place value become numbers, where each added bit doubles the range; the same bits become letters, colours, or sound only through an agreed encoding; a bit read as a truth value feeds AND, OR, NOT, which are functionally complete; and those operations, realised as gates and wired into circuits, build a half-adder and ultimately all of arithmetic. Every link rests on the one below it.