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1.4 Data types, data structures and algorithms

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do logic gates implement Boolean expressions, and how do we simplify those expressions using the laws of Boolean algebra?

Logic gates (AND, OR, NOT, XOR, NAND, NOR) and their truth tables, constructing and interpreting truth tables, and simplifying Boolean expressions using the laws of Boolean algebra including De Morgan's laws, distribution, association and commutation, and Karnaugh maps.
An OCR H446 answer on Boolean algebra and logic: the logic gates (AND, OR, NOT, XOR, NAND, NOR) and their truth tables, constructing truth tables for an expression, and simplifying Boolean expressions using the laws of Boolean algebra, De Morgan's laws and Karnaugh maps.
14 min answer →

How are very large and very small real numbers stored in a fixed number of bits, and what does normalisation achieve?

Floating-point representation of real numbers using a mantissa and an exponent (both in two's complement), normalisation of a floating-point number, and the trade-off between range and precision.
An OCR H446 answer on floating-point representation: storing real numbers with a mantissa and an exponent in two's complement, how to normalise a floating-point number, and the trade-off between range and precision when bits are divided between mantissa and exponent.
14 min answer →

How are arithmetic and memory built from logic gates using adders and flip-flops?

Logic circuits built from gates: the half adder and full adder for binary addition, and the D-type flip-flop as a single-bit memory element, including their truth tables and Boolean expressions.
An OCR H446 answer on logic circuits: the half adder and full adder that perform binary addition (with their sum and carry expressions and truth tables), and the D-type flip-flop that stores a single bit, including how these combine to build arithmetic and memory.
13 min answer →

How are positive and negative whole numbers represented in binary, and how do we convert between binary, denary and hexadecimal?

Number systems: binary, denary and hexadecimal conversion, representing negative numbers with sign and magnitude and two's complement, binary addition and subtraction, fixed-point binary fractions, and the use of hexadecimal and bitwise masks.
An OCR H446 answer on number systems: converting between binary, denary and hexadecimal, representing negative numbers with sign and magnitude and two's complement, binary addition and subtraction, fixed-point binary fractions, and the use of hexadecimal and bitwise masks.
14 min answer →