Binary Addition and Overflow

Binary Addition Rules (2 digits)

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 0 (carry 1); 1 + 1 + 1 = 1 (carry 1).

Overflow in Binary Addition

Occurs when the result exceeds the maximum value that can be represented by the given number of bits.

8-bit Binary Number

A binary number that can represent values from 0 to 255.

Addition of Three Binary Digits (Rules)

0 + 0 + 0 = 0, 0 + 0 + 1 = 1, 0 + 1 + 0 = 1, 0 + 1 + 1 = 0 (carry 1), 1 + 0 + 0 = 1, 1 + 0 + 1 = 0 (carry 1), 1 + 1 + 0 = 0 (carry 1), 1 + 1 + 1 = 1 (carry 1).

Binary Addition Example

Add 01011011 + 00111010 results in 10010101.

Carry in Binary Addition

A value that is transferred to the next higher bit position when the sum exceeds the binary base (2).

Error caused by binary overflow

When a number larger than the maximum allowed value for a fixed bit number is computed, leading to inaccurate results.

Max value in 8-bit binary

The maximum value that can be represented in 8 bits is 255.