Data representation, logic gates and Boolean simplification

Learning objectives

Convert integers between binary, denary and hexadecimal in every direction, and explain why hexadecimal is used as a compact, less error-prone way of writing binary

Explain how integers, characters, strings, images, sound and video are encoded in binary, and how choices such as character set, colour depth, resolution, sample rate and bit depth affect range, quality and file size

Describe the function, symbol and Boolean operator of the AND, OR, NOT, NAND, NOR, XOR and XNOR gates, and explain how networks of gates carry out the processing of binary data

Construct truth tables for a logic circuit, a Boolean expression or a written problem, and use them to predict outputs and to show whether two expressions are equivalent

Construct logic diagrams that combine several gates from a problem description or a Boolean expression, and write the Boolean expression that a given diagram produces

Apply the laws of Boolean algebra and Karnaugh maps to simplify Boolean expressions, and draw the reduced circuit that gives the same output