Binary Study Guide

Denary (base-10) numbers are what we use daily, consisting of digits 0-9. Binary (base-2) numbers are fundamental to computers, using only 0s and 1s. For an 8-bit binary number, there are eight positions, each representing a power of two, starting from 2^0 (1) on the rightmost side, up to 2^7 (128) on the leftmost. Converting denary to binary involves finding which powers of two sum to the denary value. Converting binary to denary means summing the values of the powers of two where a '1' appears in the binary sequence. Understanding these conversions for both unsigned numbers (0 to 255) and signed numbers using Two's Complement (-128 to +127) is crucial for comprehending how computers store and process numerical data.

Binary addition involves combining two positive binary numbers, much like decimal addition, but operating with only 0s and 1s. When the sum of two bits is 2 (e.g., 1 + 1), the result is 0 with a carry-over of 1 to the next position. Logical and arithmetic shifts are operations that move the bits of a binary number to the left or right. A logical shift fills the vacated positions with zeros. An arithmetic shift, typically used for signed numbers, preserves the sign bit when shifting right by replicating the most significant bit, and fills with zeros when shifting left.