Two's complement
Two’s complement is a fixed-width positional binary representation of signed integers in which the highest-order bit has negative weight and the remaining bits have positive weights.
Modern C
Two's complement representation encodes negative integers by complementing the corresponding positive representation and adding one, with the high-order bit indicating negativity.
- How it is used
- Explains how C interprets signed bit patterns and constructs negative values from unsigned-style arithmetic.
- How deep it goes
- Works through bit-level negation and contrasts three sign representations, but stops short of a full signed-arithmetic treatment.
- Examples
- Uses a 16-bit negation table, the identity ~A + 1, and fixed-width int64_t expressions.
- What you can do after
- Evaluate signed bit patterns and compute negative values using complement-and-add-one reasoning.
Modern C, Third Edition
Two's complement is a signed-integer representation in which the high-order bit contributes negative weight and the remaining bits contribute positive weights.
- How it is used
- Explains how C interprets signed integer bit patterns and relates them to unsigned arithmetic.
- How deep it goes
- Defines sign-bit interpretation, constructs negatives with ~A + 1, and demonstrates signed ordering across unsigned representations.
- Examples
- Uses 16-bit negation of 240 and functions that classify and compare unsigned values as signed.
- What you can do after
- Evaluate signedness and signed ordering from unsigned bit patterns, and construct negatives with bitwise operations.
Read how Modern C, Third Edition explains two's complement →
Clojure: The Essential Reference
Two's complement is a binary representation of signed integers in which negative values are encoded by complementing the bits of their magnitudes and adding one.
- How it is used
- Explains signed integer overflow and bit-shift behavior in Clojure's numeric and bitwise operations.
- How deep it goes
- Works through 32-bit and 64-bit boundary layouts, then applies the representation to arithmetic and logical shifts.
- Examples
- Uses 32-bit and 64-bit boundary tables plus binary-string demonstrations of negative right shifts.
- What you can do after
- Evaluate signed overflow and interpret arithmetic versus unsigned right shifts in Clojure.
Read how Clojure: The Essential Reference explains two's complement →
Building Quantum Software with Python
Two's complement is a signed binary representation in which the leading bit distinguishes nonnegative values from negative values and an m-bit string represents values from −2^(m−1) through 2^(m−1)−1.
- How it is used
- Represents negative outputs in fixed-width quantum value registers and supports searches for nonnegative function outcomes.
- How deep it goes
- Defines sign-bit ranges and demonstrates four-bit encodings, but does not derive two's complement arithmetic.
- Examples
- Uses f(k)=k²−3 with output 1101 for −3 and f(k)=k²−5 with a four-qubit range from −8 through 7.
- What you can do after
- Apply it via build_polynomial_circuit, grid_state, and oracle_match_0 to encode and search signed quantum function outputs.
Read how Building Quantum Software with Python explains two's complement →
Related concepts
- sign representationkind of · A sign representation is a scheme for encoding the sign and magnitude of a signed numerical value in bits.
- binary stringuses · A binary string is a finite, ordered sequence of binary digits, each having the value zero or one.
- integerimplements · An integer is a whole-number value with no fractional part, including negative numbers, zero, and positive numbers.
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