Where NOT applies in an expression
Name:
Date:
Class:
A
Quick Questions
Shade in the A or B circle for each question.
1. In X = NOT (A AND B), what does NOT apply to?
2. In X = (NOT A) AND B, what does NOT apply to?
3. A = 1 and B = 1. Which expression gives X = 0?
4. A = 0 and B = 1. Which expression gives X = 1?
5. A = 1 and B = 0. Which expression gives X = 1?
B
Match the Pairs
Draw a line connecting each item on the left to its match on the right.
| Left column | Right column | |
|---|---|---|
| 1(NOT A) AND B | ANOT flips only input A first. The result of that is then ANDed with B. | |
| 2NOT (A AND B) | BX = NOT (A AND B) | |
| 3NOT applies to the input A alone, and B is not changed before the AND | CA AND B is worked out first. NOT then flips the whole result of the bracket. | |
| 4NOT is applied to the output of an AND gate, so it flips the result of the bracket | DThe brackets are placed round A AND B, so NOT flips the final output. The student wanted NOT on input A only. | |
| 5X = NOT A AND B (meant: NOT (A AND B)) | EThe brackets are missing, so NOT applies only to A. The student wanted NOT to flip the whole result of A AND B. | |
| 6X = NOT (A AND B) (meant: (NOT A) AND B) | FX = (NOT A) AND B |
C
Definitions
NOT (A AND B)
D
Fill in the Blanks
Complete each line of code by filling in the missing parts.
1.
X = ___ (A AND B)
2.
X = (NOT A) ___ B
3.
X = (NOT _) AND B
4.
When A = 1 and B = 0:
NOT (A AND B) = _
5.
When A = 1 and B = 0:
(NOT A) AND B = _
E
Spot the Error
Shade in the letter of the line that contains an error.
Question 1
A
# A=1, B=0, so X must be 1
B
X = (NOT A) AND B
C
# bracket = 0, NOT gives 1
Question 2
A
# A=1, B=0, so X must be 0
B
# NOT flips only input A
C
X = NOT (A AND B)
Question 3
A
a = True
B
b = False
C
x = not a and b
D
print(x) # True
Question 4
A
A = 0, B = 0
B
A AND B = 0
C
NOT (A AND B) = 1
D
(NOT A) AND B = 1
Question 5
A
A = 1, B = 1
B
A AND B = 1
C
NOT (A AND B) = 1
D
(NOT A) AND B = 0
Answer Key
Where NOT applies in an expression
Section A: Quick Questions
Q1
A — The output of the bracket (A AND B)
Q2
A — Only input A
Q3
B — NOT (A AND B)
Q4
B — (NOT A) AND B
Q5
A — NOT (A AND B)
Section B: Match the Pairs
Q1
(NOT A) AND B → NOT flips only input A first. The result of that is then ANDed with B.
Q2
NOT (A AND B) → A AND B is worked out first. NOT then flips the whole result of the bracket.
Q3
NOT applies to the input A alone, and B is not changed before the AND → X = (NOT A) AND B
Q4
NOT is applied to the output of an AND gate, so it flips the result of the bracket → X = NOT (A AND B)
Q5
X = NOT A AND B (meant: NOT (A AND B)) → The brackets are missing, so NOT applies only to A. The student wanted NOT to flip the whole result of A AND B.
Q6
X = NOT (A AND B) (meant: (NOT A) AND B) → The brackets are placed round A AND B, so NOT flips the final output. The student wanted NOT on input A only.
Section C: Definitions
Q1
NOT (A AND B) — NOT before a bracket flips the whole bracket's result. In (NOT A) AND B, NOT flips only input A, so NOT (A AND B) gives different results.Section D: Fill in the Blanks
Q1
X = NOT (A AND B)Q2
X = (NOT A) AND BQ3
X = (NOT A) AND BQ4
When A = 1 and B = 0:
NOT (A AND B) = 1Q5
When A = 1 and B = 0:
(NOT A) AND B = 0Section E: Spot the Error
Q1
B — NOT must go before the bracket so it flips the whole result of A AND B. (NOT A) AND B only flips A, giving 0 here instead of 1. It should be X = NOT (A AND B).
Q2
C — The comment says NOT applies to input A only, so A needs its own brackets: (NOT A) AND B. NOT (A AND B) flips the whole bracket and gives 1, not 0.
Q3
C — Without brackets, not applies only to a, so the result is False. To flip the whole result of a and b, write x = not (a and b), which gives True.
Q4
D — NOT A is 1 and B is 0, so 1 AND 0 = 0. The answer should be (NOT A) AND B = 0, which differs from NOT (A AND B) = 1.
Q5
C — A AND B is 1, and NOT flips the bracket's result, so NOT (A AND B) = 0, not 1.