MS1 Chapter 1: Number Representation

The most common tool used worldwide to process information and represent data, and is essential to understanding how computers operate.

The use of two distinct values, 0 and 1, to represent and work with information, especially numbers. This is the fundamental basis of computer operations.

The size of the numbers a computer can handle is restricted due to limitations in storage space, ultimately defining limits on the computer's ability to express numbers.

A system of representing numbers using a specific number of digits (symbols), with a 'base' that determines the number of digits used. For example, in base 10, we use digits 0-9.

The process of converting a number from a given base (like base 10) to another base (like base 2) involves repeated division by the new base and noting the remainders. The remainders, read from right to left, form the representation in the new base.

The process of calculating the value of a number expressed in base B involves multiplying each digit by increasing powers of the base (starting from zero) from right to left, and then summing the results.

The conversion of a binary number to an octal (base 8) involves grouping the binary digits into sets of 3 bits, starting from the right. Each group is then replaced by its equivalent octal digit.

The conversion of a binary number to a hexadecimal (base 16) involves grouping the binary digits into sets of 4 bits, starting from the right. Each group is then replaced by its equivalent hexadecimal digit.

The process of adding two binary numbers involves adding each pair of bits individually, taking into account any carry-over. The carry-over from one position is added to the next.

The process of subtracting two binary numbers involves subtracting each pair of bits individually, taking into account any borrow from higher positions.

The process of multiplying two binary numbers involves multiplying each bit of one number by the other, and then adding the partial products together.

Methods for representing negative integer numbers in a computer system.

A method for representing negative numbers where a sign bit is used to indicate positive (0) or negative (1), and the remaining bits represent the absolute value. However, it makes arithmetic calculations complicated.

A method for representing negative integers where a negative integer is obtained by flipping all the bits in the binary code of its positive counterpart.

A method for representing negative integers where the negative number is derived by adding 1 to its 1's complement representation.

A method for representing real numbers in a computer, where the number is stored as a mantissa (a decimal part) and an exponent, allowing for representation of a wide range of numbers.

A standard established by the IEEE (Institute of Electrical and Electronics Engineers) for representing floating-point numbers in single precision (32 bits), using a sign bit, an exponent, and a mantisa, ensuring consistency in numerical representation across different systems.

A code commonly used to represent alphanumeric characters on computers, including letters, numbers, punctuation marks, and control characters.

A code designed to support a wider range of characters and symbols than the original ASCII code, mainly for supporting multiple languages and special characters.

A coding scheme where a single bit change in the binary representation of a number results in a single bit change in its Gray code representation, making it useful in systems where changes need to be tracked smoothly, like digital sensors.

A code used to represent base 10 digits, where each decimal digit is represented by its equivalent four-bit binary value, providing a method for representing decimal numbers in a binary system.

A mathematical system that forms the foundation for digital logic circuits, working with binary variables (0 and 1) and logical operators (AND, OR, NOT) to represent and manipulate logical relationships.

The basic building blocks that form Boolean expressions.

An expression formed by combining Boolean variables with Boolean operators, resulting in a true or false value when evaluated.

A table that represents all possible combinations of input values (variables) and their corresponding output values (function results) for a Boolean expression.

A mathematical function that takes Boolean variables as input and outputs a Boolean value determined by the logical operations applied to those variables.

A standard form for representing Boolean functions that involves combining product terms (AND operations) using the OR operator (sum).

A standard form for representing Boolean functions that involves combining sum terms (OR operations) using the AND operator (product).

A type of Boolean function where each term includes all variables of the function, either in their original form or complemented, allowing for a systematic way to represent the function.

A process for obtaining the canonical forms of a Boolean function, by either finding the

A compact way to represent the canonical SOP form of a Boolean function, by assigning a decimal value to each min-term based on the binary representation of the corresponding variable values.

A compact way to represent the canonical POS form of a Boolean function, by assigning a decimal value to each max-term based on the binary representation of the corresponding variable values.

A function where at least one combination of input values does not have a defined output value, making it incomplete.

The process of simplifying Boolean expressions or functions to a more compact form, typically requiring fewer logic gates, optimizing circuit implementation, and reducing cost.

A simplification method that involves applying Boolean algebra theorems (laws and postulates) to replace equivalent expressions and eliminate redundant terms.

A visual method for simplifying Boolean functions using a table-like diagram (Karnaugh map) that represents min-terms and max-terms, allowing for easy identification of adjacency and grouping of terms.