Lessons 4–5 · 2 lessons · M. R. Fayziyeva, D. M. Sayfurov, N. S. Xaytullayeva. Informatics and Information Technologies, Grade 9. “Nashriyot uyi Tasvir”, Tashkent, 2020
4
Logic circuits
Textbook: pp. 13–15
GoalKnows the basic logic elements (AND, OR, NOT), builds a logic circuit for an expression and finds the output signal of a circuit.
New words
logic element: a device that processes binary signals and carries out one logical operation · mantiqiy elementconjunctor (AND element): output 1 only if all inputs are 1 · konyunktordisjunctor (OR element): output 1 if at least one input is 1 · dizyunktorinverter (NOT element): output is the opposite of the input · invertor
Explanation
Computers, phones and other digital devices are built from logic elements. A signal that is present counts as 1, no signal counts as 0. A conjunctor (“AND”) has at least two inputs and gives 1 at the output only if every input is 1. A disjunctor (“OR”) gives 1 if at least one input is 1. An inverter (“NOT”) has one input and turns the signal into its opposite. A logic circuit is a device made of several connected elements that performs some logical function. To draw a circuit: find the number of variables, fix the order of the operations, choose an element for each operation, and connect the elements in that order.
Worked examples
Circuit for A ∧ ¬B: input B goes to an inverter; the inverter output and A go to a conjunctor. With A = 1, B = 0 the inverter gives 1 and the conjunctor gives 1 ∧ 1 = 1.
Circuit: A and B go to a disjunctor whose output goes to an inverter; the output is X. So X = ¬(A ∨ B). For (A,B) = 00, 01, 10, 11 we get X = 1, 0, 0, 0 – there is an output signal only when neither input has a signal.
Class activity
“Human circuit”: three students play the elements AND, OR, NOT. An input signal is a raised hand (1). The class gives an expression and the “elements” raise or lower their hands in turn.
Practice
1
Name the three basic logic elements and the operation each performs.