Egypt Secondary 3 Communication Technology, Week 11: Two switches side by side: the OR gate

The OR gate

Week 11 · Unit 2 Topic 4: the OR gate: parallel switches, symbol, number of forms, truth table, Boolean formula · 3 lessons

Two switches side by side: the OR gate

ICT Secondary 3 Term 1, Unit 2, Topic 4: pp. 40–47

GoalExplain why two switches side by side light the lamp when at least one is closed, and write this as a rule.

New words

in parallel · side by side, each on its own wire, so the current can take either pathpath · a route the current can follow from the source through the lampOR gate · a gate whose output is 1 when at least one input is 1at least one · one or more: one input, or two, or all of them

Explanation

In Week 8 two switches in a row made a single path, and one open switch broke it. Now put the two switches side by side: each switch has its own wire to the lamp, so there are two paths, and the current needs only one complete path. If A is closed the lamp is lit, whatever B does. If B is closed it is lit, whatever A does. If both are closed it is lit as well. The lamp is unlit only when both switches are open, because then both paths are broken. Write closed as 1 and open as 0: the lamp is 1 when A is 1, or B is 1, or both are. This is the OR gate. Opening one switch of a parallel pair does not break the circuit, because the other path is still there. Three switches side by side follow the same idea: one closed switch is enough. The OR rule in words is: the output is 1 if at least one input is 1. Note that in this rule “or” includes “both”.

Switch A	Switch B	Complete paths	Lamp
open	open	none	unlit
open	closed	through B	lit
closed	open	through A	lit
closed	closed	through A and through B	lit

Worked examples

Teacher’s key turned	Librarian’s key turned	Room
no	no	stays locked
no	yes	opens
yes	no	opens
yes	yes	opens

An everyday OR rule (invented): the club room opens if the teacher has turned a key or the librarian has turned a key.

A	B	C	Lamp
open	open	open	unlit
open	open	closed	lit
closed	open	closed	lit
closed	closed	closed	lit

Three switches side by side. A single closed switch is enough, so the lamp is unlit only when all three are open.

Compare the two wirings. In a row there is one path and any open switch breaks it, so AND needs every switch closed. Side by side there are several paths and one is enough, so OR needs just one. Of the eight ways to set three switches side by side, seven light the lamp.

Class activity

Draw on paper two switches side by side with a lamp. Label them A, B and L and colour the complete paths for each of the four states. Write which states light the lamp. Then draw three switches side by side and count how many of the eight states leave the lamp unlit.

Practice

Two switches are side by side, A is open and B is closed. Is the lamp lit?

When is the lamp of two parallel switches unlit?

Say the OR rule in words.

A door chime sounds if the front button or the side button is pressed. Which gate is this, and what are its inputs?