A digital synthesizer uses a binary representation to store discrete control values for a filter sweep. The system must be capable of representing at least 10,000 10,000\,10,000 unique states to ensure smooth parameter transitions.
Identify the minimum number of bits required to represent at least 10,000 10,000\,10,000 unique states, and the total number of distinct states that this minimum number of bits can actually represent.
13 bits, representing 8,1928,1928,192 unique states
14 bits, representing 16,38416,38416,384 unique states
14 bits, representing 28,00028,00028,000 unique states
10 bits, representing 1,0241,0241,024 unique states
117 exam-style questions on Edexcel GCSE Computer Science Binary, covering Binary representation and number of states, Unsigned and two's complement integers, Converting denary and 8-bit binary, Binary addition and binary shifts, Concept of overflow, and Hexadecimal notation and conversion. Each one has a worked solution and a mark scheme showing where the marks go.