54 Definition The binary system is a numerical system which uses only two digits, 1 and 0. The two digits symbolise respectively the on/off state of a circuit, or true/false information in logic gates, and they can be used to represent all the existing real numbers when put in a particular sequence in which each position is a power of 2. So, the 1s and 0s, according to their position, are multiplied by the corresponding power of two. The sum of the resulting values equals the number represented, which simply appears as a string of 0s and 1s . How would you represent, for example, numbers 1, 15, and 23 in the binary system? For example, the quantity of data which can be handled by a computer processor is usually expressed in bits. Bytes are normally employed as measuring units of the dimensions of files and computer memory. Who was George Boole? Search the Internet for information about him and the system called Boolean algebra. Bits and bytes The two digits 0 and 1 in the binary system are called bits (short for Binary Digit) and are the smallest data units of the system. The strings they are arranged and in are called words; words containing 8 bits are called bytes. Bits (b) and bytes and (B) are used as measuring units in information technology . To perform more complex operations, logic gates can be combined in groups and have more than two inputs. and power: potenza to reverse: invertire string: sequenza THE BINARY SYSTEM AND LOGIC GATES Logic gates Logic gates are digital circuits, whose functioning is based on the 1 and and 0, true/ false system governing the binary or system. Logic gates are designed to or Boolean perform specific tasks; based on algebra , they have one or two inputs and or NOT IN nand OUT 1 0 or NAND not 0 1 and AND or IN IN OUT IN IN OUT 0 0 1 1 0 1 0 1 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 not and OR EXCLUSIVE OR IN IN OUT IN IN OUT 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 0 1 0 1 1 0 not or not and a single output, which is the product of a series of instructions that follow a precise logic. According to their logic, circuits are named basic logic gates NOT, AND, OR or derived logic gates NAND, NOR, XOR, XNOR. Types of logic gates AND gate: the output is true only when both inputs are true. NOT gate: it is also called inverter because it reverses the logic state, and it is the simplest gate because it has only one input. If the input is true, the output is false and vice-versa. OR gate: the output is true if either or both of the inputs are true. NAND gate: it acts in the manner of the logical operation AND followed by a negation. The output is false if both inputs are true. NOR gate: its output is true if both inputs are false. XOR gate: the output is true if either, but not both, of the inputs is true. XNOR gate: it is a combination of an XOR gate followed by an inverter. Its nand output is true if the inputs are the same. The logic gates have symbolic nand representations which are often accompanied by their truth tables. A truth table is a representationnorof all possible combinations of true and false with their outputs. nand nor nor nand NOR not nor xor xor IN IN OUT 0 0 1 1 0 1 0 1 1 0 0 0 nor xor EXCLUSIVE NOR nand or 128 ELECTRONICS AND ELECTROTECHNOLOGY nand xnor xor IN IN OUT 0 0 1 1 0 1 0 1 1 0 0 1 xnor xnor xor