15.2 Boolean Algebra & Logic Circuits
A Level · 3 questions found
What this topic covers
Section titled “What this topic covers”- Truth tables for complex circuits including half-adders and full-adders
- Flip-flops (SR, JK): draw circuit, derive truth table, use as data storage
- De Morgan’s laws: understand, apply and use to simplify
- Simplify logic circuits/expressions using Boolean algebra
- Karnaugh maps (K-maps): purpose, benefits and solving logic problems
Past paper questions
Section titled “Past paper questions” Q6
6
The diagram shows a logic circuit.
A
B
C
P
R
Q
S
Z
(a) Complete the truth table for the given logic circuit.
Show your working.
Working space
A
B
C
P
Q
R
S
Z
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
[3]
(b) Write the Boolean expression that corresponds to the logic circuit as a sum-of-products.
Z = ............................................................................................................................................
............................................................................................................................................. [2]
(c) (i) Complete the Karnaugh map (K-map) for the Boolean expression:
A.B.C + A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
00
0
A
BC
1
01
11
10
[2]
(ii) Draw loop(s) around appropriate group(s) in the K-map to produce an optimal
sum-of-products.
[2]
(iii) Write the Boolean expression from your answer to part (c)(ii) as a simplified
sum-of-products.
..................................................................................................................................... [1]
Show mark scheme
6(a) [3 marks]
mark for working, all four columns P, Q, R and S
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
Z
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
Z
6(b) [2 marks]
marks for all five correct terms and no extras
mark for any three correct terms
(Z =) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
mark for any three correct terms
(Z =) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
6(c)(i) [2 marks]
marks if all correct
mark if one error present
00
01
11
10
BC
mark if one error present
00
01
11
10
BC
6(c)(ii) [2 marks]
mark for each correct loop
(Max 2)
00
01
11
10
BC
(Max 2)
00
01
11
10
BC
Q6
6
The diagram shows a logic circuit.
A
P
Q
R
S
T
Z
B
C
(a) Complete the truth table for the given logic circuit.
Show your working.
Working space
A
B
C
P
Q
R
S
T
Z
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
[3]
(b) Write the Boolean expression that corresponds to the logic circuit as a sum-of-products.
Z = ............................................................................................................................................
............................................................................................................................................. [2]
(c) (i) Complete the Karnaugh map (K-map) for this Boolean expression:
A–.B–.C– + A–.B.C– + A–.B.C + A.B–.C– + A.B.C– + A.B.C
00
01
11
10
0
1
[2]
(ii) Draw loop(s) around appropriate group(s) in the K-map to produce an optimal
sum-of-products.
[2]
(iii) Write the Boolean expression from your answer to part c(ii) as a simplified
sum-of-products.
..................................................................................................................................... [1]
BC
A
Show mark scheme
6(a) [3 marks]
mark for working, all five columns P, Q, R, S and T
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
T
Z
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
T
Z
6(b) [2 marks]
marks for all six correct terms only
mark for any three correct terms
(Z = ) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
mark for any three correct terms
(Z = ) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
6(c)(i) [2 marks]
marks if all correct
mark if only one error present
00
01
11
10
0
1
0
1
1
1
1
0
1
1
A
BC
mark if only one error present
00
01
11
10
0
1
0
1
1
1
1
0
1
1
A
BC
6(c)(ii) [2 marks]
mark for each correct loop
(Max 2)
00
01
11
10
0
1
0
1
1
1
1
0
1
1
BC
A
(Max 2)
00
01
11
10
0
1
0
1
1
1
1
0
1
1
BC
A
Q6
6
The diagram shows a logic circuit.
A
B
C
P
R
Q
S
Z
(a) Complete the truth table for the given logic circuit.
Show your working.
Working space
A
B
C
P
Q
R
S
Z
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
[3]
(b) Write the Boolean expression that corresponds to the logic circuit as a sum-of-products.
Z = ............................................................................................................................................
............................................................................................................................................. [2]
(c) (i) Complete the Karnaugh map (K-map) for the Boolean expression:
A.B.C + A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
00
0
A
BC
1
01
11
10
[2]
(ii) Draw loop(s) around appropriate group(s) in the K-map to produce an optimal
sum-of-products.
[2]
(iii) Write the Boolean expression from your answer to part (c)(ii) as a simplified
sum-of-products.
..................................................................................................................................... [1]
,
,
Show mark scheme
6(a) [3 marks]
mark for working, all four columns P, Q, R and S
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
Z
mark for first four rows of column Z
mark for second four rows of column Z
Working space
B
C
P
Q
R
S
Z
6(b) [2 marks]
marks for all five correct terms and no extras
mark for any three correct terms
(Z =) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
mark for any three correct terms
(Z =) A.B.C + A.B.C + A.B.C + A.B.C + A.B.C
6(c)(i) [2 marks]
marks if all correct
mark if one error present
00
01
11
10
BC
mark if one error present
00
01
11
10
BC
6(c)(ii) [2 marks]
mark for each correct loop
(Max 2)
00
01
11
10
BC
(Max 2)
00
01
11
10
BC