Computer Science A2 · Hardware and Virtual Machines. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Logic circuits can add and can store. A half adder adds two bits and gives a sum and a carry. A full adder adds two bits and a carry-in, so full adders can be joined to add whole binary numbers.
A flip-flop is a circuit with feedback that holds its output until it is changed, so it stores one bit. The SR and JK types are the ones to know.
A Boolean expression can be made simpler, which means fewer gates. This is done with the laws of Boolean algebra, including De Morgan's laws, or with a Karnaugh map, where 1s in adjacent cells are grouped and the variable that changes inside a group is removed.
With De Morgan's laws students put NOT on each term but forget to change the operator. Breaking the bar always swaps AND with OR: NOT (A AND B) becomes (NOT A) OR (NOT B), never (NOT A) AND (NOT B).
Answer: X = NOT A (check: X is 1 for A = 0 with B = 0 or 1, and 0 for A = 1).
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