Answers

F9.1 Logic gates and truth tables

Logic and computer systems · GCSE · OCR J277 2.4.1, AQA 8525 3.4.2, Edexcel 1CP2 1.3.1 · about 15 min

What this lesson is about

AND, OR and NOT, their symbols and truth tables, and a robot decision as a circuit.

• AND, OR and NOT
• Truth tables
• A robot decision as a circuit
• Three inputs

Questions 6 marks in all

1. [1 mark]When does an AND gate output 1?

   1. AOnly when both inputs are 1
   2. BWhen at least one input is 1
   3. CWhen the inputs are different
   4. DWhen both inputs are 0
   Answer: A. AND needs both inputs on.

2. [1 mark]When does an OR gate output 0?

   1. AOnly when both inputs are 0
   2. BWhen at least one input is 0
   3. CWhen the inputs are different
   4. DNever
   Answer: A. OR is 1 if any input is 1, so it is 0 only when both are 0.

3. [1 mark]How many rows does a truth table for 3 inputs have?

   Answer: 8. 2 × 2 × 2 = 8 combinations.

4. [1 mark]A is 1 and B is 1. What is A AND (NOT B)?

   Answer: 0. NOT B is 0, and 1 AND 0 is 0.

5. [1 mark]What does this program print?

   def AND(a, b): return 1 if a and b else 0
   def NOT(a): return 1 - a
   print(AND(1, NOT(0)), NOT(AND(1, 1)))

   Answer:

   1 0

   NOT 0 is 1, so AND(1, 1) is 1; AND(1, 1) is 1, so NOT gives 0.

6. [1 mark]Which gate has only one input?

   1. ANOT
   2. BAND
   3. COR
   4. DXOR
   Answer: A. NOT flips a single input.

The task: truth tables

# the two lines every program starts with: the commands, then the robot
from bugbot import *
connect()

def AND(a, b):
    return 0

from bugbot import *
connect()
def AND(a, b):
    return 1 if a == 1 and b == 1 else 0

def OR(a, b):
    return 1 if a == 1 or b == 1 else 0

def NOT(a):
    return 1 - a

for a in [0, 1]:
    for b in [0, 1]:
        print(f"A={a} B={b} Q={AND(a, NOT(b))}")