created: 07/04/96; 2^{nd} edition: 05/26/01;
additions: 09/25/01; audio: 09/20/03

Digital computers use bit patterns to represent many types of data. Various operations can be performed on data. Computers perform operations on bit patterns. With a good representation scheme, bit patterns represent data and bit pattern manipulations represent operations on data.

An important example of this is the Binary Addition Algorithm, where two bit patterns representing two integers are manipulated to create a third pattern which represents the sum of the integers.

**Chapter Topics:**

- Single-bit Binary Addition Table.
- Binary Addition Algorithm.
- Addition in Hexadecimal Representation.
- Overflow
- Sign-magnitude Representation.
- Two's complement Representation.
- How to negate an integer in Two's Complement Representation.
- The two's compement sign bit.
- Overflow detection in unsigned binary.
- Overflow detection in two's complement binary.

Most processor chips implement the Binary Addition Algorithm in silicon as part of their arithmetic logic unit. In a course in digital electronics you will study the hardware details of its implementation. This chapter discusses the fundamentals of the algorithm.

Compute the following. Give the answer in binary notation.

0 + 0 = ? 0 + 1 = ? 1 + 0 = ? 1 + 1 = ?