algorithms

How the Computer Subtracts by Adding: Two's Complement and Overflow

2026-03-27·4958 words·24 mins

Number Systems binary overflow hexadecimal Python algorithms

To subtract, the processor adds the first number to the complement of the second, so a single adder does both operations. We will see two’s complement, why 8 signed bits range from -128 to +127, and how overflow took down the Ariane 5 and froze Pac-Man on level 256.

Computer Arithmetic: Addition and Subtraction in Binary, Octal, and Hexadecimal

2026-03-25·4718 words·23 mins

Number Systems logic binary hexadecimal octal decimal algorithms Python

The addition and subtraction rules of base 10 hold in any base: only the value that triggers the carry changes. We do arithmetic in binary, octal, and hexadecimal, see why with three addends the carry can be worth 2, and implement both algorithms in Python.

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