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neurologyYou need to know

• Primitive data types include integer for whole numbers, real or floating point for values with fractional parts, character for one symbol, string for a sequence of characters, and Boolean for the values true and false.
• Binary is a base-two number system using the digits 0 and 1, and each position in an unsigned binary integer has a place value that is a power of two.
• Hexadecimal is a base-sixteen number system using the digits 0–9 and A–F, where A–F represent denary 10–15, and one hexadecimal digit corresponds exactly to four binary bits.
• In sign-and-magnitude representation, the most significant bit stores the sign and the remaining bits store the magnitude; zero therefore has both positive and negative representations.
• In an 𝑛-bit two's complement integer, negative values are formed by inverting every bit of the positive value and adding 1, giving the range −2𝑛−1 to 2𝑛−1 −1.
• Binary addition follows the same place-value method as denary addition, with 1 +1 =10; subtraction can be performed by adding the two's complement of the value being subtracted.
• Overflow occurs when the result of binary arithmetic lies outside the range representable by the available number of bits, such as adding two positive two's complement numbers and obtaining a negative result.
• A binary floating-point number stores a mantissa and an exponent, with the exponent determining how far the binary point is shifted; limited mantissa and exponent sizes restrict precision and range.
• A two's complement floating-point mantissa is normalised when its first two bits are different, which maximises the precision available without changing the represented value.
• Floating-point addition and subtraction require the exponents to be aligned before the mantissas are combined, after which the result may need to be normalised; rounding can introduce representation errors.
• Bitwise AND produces 1 only where both corresponding bits are 1, OR produces 1 where either bit is 1, XOR produces 1 where the bits differ, and masks use these operations to inspect, set, clear or toggle selected bits.
• A left shift moves bits towards more significant positions and usually multiplies an unsigned integer by a power of two, while a right shift moves bits towards less significant positions and usually performs integer division by a power of two; discarded bits are lost.
• Character sets assign numerical codes to characters: ASCII represents a limited set of characters, while Unicode provides code points for characters and symbols from many writing systems.
• An array stores elements of the same data type in indexed positions and may have up to three dimensions, whereas a record groups related fields that may have different data types.
• A list is an ordered, mutable collection, while a tuple is an ordered collection that is normally immutable; a linked list stores each item in a node containing data and one or more links to other nodes.
• A stack is a last-in, first-out structure using push, pop and peek operations, whereas a queue is a first-in, first-out structure using enqueue, dequeue and front operations.
• A graph consists of vertices connected by edges; directed graphs have edges with a direction, while undirected graphs have edges that can be followed in either direction.
• A tree is a hierarchical structure of nodes, and a binary search tree places values smaller than a node in its left subtree and larger values in its right subtree, enabling an in-order traversal to produce sorted data.
• A hash table applies a hash function to a key to calculate a storage location, and collisions must be handled using a method such as chaining or open addressing.
• Boolean algebra operates on true and false values: AND requires both inputs to be true, OR requires at least one true input, NOT reverses an input, and XOR is true when its inputs differ; Boolean expressions can be simplified using commutation, association, distribution, double negation, De Morgan's laws and Karnaugh maps, while D-type flip-flops store one bit, half adders add two bits, and full adders add two bits plus a carry-in.

• Convert positive integers accurately between denary, binary and hexadecimal, grouping binary digits into sets of four when converting to or from hexadecimal.
• Represent positive and negative integers using fixed-width sign-and-magnitude and two's complement notation, checking that each value is within the available range.
• Add and subtract fixed-width binary integers, using two's complement for subtraction and identifying any overflow.
• Represent, normalise, add and subtract positive and negative binary floating-point numbers by aligning exponents, combining mantissas and renormalising the result.
• Apply left and right shifts and use AND, OR and XOR masks to test, set, clear or toggle specified bits.
• Encode and decode text using supplied ASCII or Unicode character codes.
• Create, traverse, search, insert into and remove data from arrays, records, lists, tuples, linked lists, graphs, stacks, queues, trees, binary search trees and hash tables using suitable algorithms.
• Translate logical requirements into Boolean expressions, logic-gate diagrams and complete truth tables.
• Simplify Boolean expressions using De Morgan's laws, distribution, association, commutation, double negation and correctly grouped Karnaugh maps.
• Construct and interpret truth tables and logic diagrams for D-type flip-flops, half adders and full adders, including sum, carry and stored-output behaviour.