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Everything about Redundant binary representation

A redundant binary representation (RBR) is a numeral system that uses more bits than needed to represent a single binary digit so that most numbers have several representations. An RBR is unlike usual binary numeral systems, including two's complement, which use a single bit for each digit. Many of an RBR's properties differ from those of regular binary representation systems. Most importantly, an RBR allows addition without using a typical carry. When compared to non-redundant representation, an RBR makes bitwise logical operation slower, but arithmetic operations are faster when a greater bit width is used. Usually, each digit has its own sign that is not necessarily the same as the sign of the number represented. When digits have signs, that RBR is also a signed-digit representation. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Redundant binary representationA 5-minute orientation
  2. Skim a recent paper: A Scalable Montgomery Modular Multiplication Architecture with Low Area-Time Product Based on Redundant Binary RepresentationInfluential work since 2022
  3. Pick up a classic book: Data Communications and NetworkingThe most-reprinted book on the subject
  4. Read the landmark paper: Accurate rounding scheme for the Newton-Raphson method using redundant binary representationCited 34 times
  5. Go sideways: Signed number representationsA closely related topic
  6. Go sideways: Bitwise operationA closely related topic

📖 Definitions

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🗂️ The subject at a glance

  1. Conversion from RBR
  2. Example of redundant binary representation
  3. Arithmetic operations
  4. Logical operations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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🔗 Related topics