Page | 126

Chapter 3

Binary Logic
1.3.1Binary Logic

Have Read
To Revise

Prepared
S No Learning Outcome To Read

Revised
Have
1.3.1: Logic gates
22 use logic gates to create electronic circuits
Understand and define the functions of NOT, AND, OR, NAND, NOR
and XOR (EOR) gates, including the binary output produced from all
23
the possible binary inputs (all gates, except the NOT gate, will have 2
inputs only)
24 Draw truth tables and recognise a logic gate from its truth table
25 Produce truth tables for given logic circuits,
Produce a logic circuit to solve a given problem or to implement a
26
given written logic statement
27 Write down logic statement of given logic circuit
28 Simplify the logic circuit
29 Boolean algebra
30 Solving past paper questions
Page | 127
1.3.1 Logic Gates
Many electronic circuits have to make decisions. They look at two or more inputs and
use these to determine the outputs from the circuit. The process of doing this uses electronic logic,
which is based on digital switches called Logical Gates.
Logic gates are devices that can combine multiple inputs at independent logic levels and come up
with an output accordingly. They are used by implementing Boolean algebra. Logic gates have two
or more input and one output except NOT Gate which has one input and one output.
The most common Logical Gates are given below:

For example, The most obvious use is for simple control. Imagine designing a washing machine
so that the water only turns on when the washing is loaded (logic-1), the door is closed (logic-1)
but the clothes are not yet wet (logic-0). This can be done by ANDing the first two conditions, and
inverting the third. Now, AND these together, and you get a high only when all three conditions are
satisfied.
Two or more logic gates can be connected to produce a logic circuit with one or more outputs from
two or more inputs.

Truth Tables:
“A truth table is used to show the output of a logic gate or circuit for all possible combinations of
input values.”
Usually the binary values are used, 1 and 0, as shorthand for True and False.
The truth table for a two-input gate needs four rows (2 2=4) while for 3-input gate needs eight rows
(23=8).
Page | 128
1) NOT Gate (Inverter):
A NOT gate or an inverter is the simplest kind of logic gate. Its function is to give the opposite
output to its input - if it gets a high (1), it gives a low (0), and vice versa.
This is equivalent to saying that the output is not the input.
NOT Gate
Input A Output X
0 1
1 0
The output X) =1 if
INPUT A is NOT 1(i.e. 0 or OFF).
𝑿=𝑨

2) AND Gate
An AND gate gives an output 1 only when both inputs are 1.
If one or more inputs are 0, then the output is also 0.

Input A Input B Output x

0 0 0
0 1 0
1 0 0
1 1 1

The output (called X) is true (i.e. 1 or ON) only if the (INPUT A AND INPUT B) are both true (i.e. 1
or ON).
The x=1 if
INPUT A is 1 AND INPUT B is 1
𝑿=𝑨.𝑩

3) OR Gate
An OR gate gives a high (1) output if any input is high (1). If all inputs are low (0), then the output
is low (0).
Input A Input B Output x
0 0 0
0 1 1
1 0 1
1 1 1

The output (called X) is true (i.e. 1 or ON) if the (INPUT A OR INPUT B) are true (i.e. 1 or ON).
The OUTPUT X=1 IF
Either INPUT A is 1
OR INPUT B is 1
𝑿=𝑨+𝑩
Page | 129
4) NAND Gate
This NOT AND combination is shortened to just NAND. A NAND gate gives a 0 output only when
both inputs are 1. If one or more inputs are 0, then the output is 1.
Input A Input B A AND B OUTPUT X
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
The output (called X) is true (i.e. 1 or ON) if
(INPUT A AND INPUT B) are NOT both true (i.e. 1 or ON). Is 1
𝑿=𝑨. 𝑩

5) NOR Gate
This NOT OR combination is shortened to just NOR. A NOR gate gives a 1 output only if no inputs
are 1. If an input is 0, then the output is 0.

Input A Input B A OR B OUTPUT X

0 0 0 1
0 1 1 0
1 0 1 0
1 1 1 0
The OUTPUT x=0 IF
Either INPUT A is 1 OR INPUT B is 1
𝑿=𝑨+ 𝑩

6) XOR Gate
The 'Exclusive-OR' gate is a circuit which will give a 1 output if either, but not both, of its two
inputs are 1. If both inputs are same then output will be 0 else output will be 1

Input A Input B Output x

0 0 0
0 1 1
1 0 1
The OUTPUT X=1 IF 1 1 0
Either A is 1 AND B is NOT 1
OR A is NOT 1 AND B is 1
Or it may be said that X=1 If A is 1 OR B is 1 BUT NOT BOTH
𝑿 = (𝑨 . 𝑩) + (𝑨 . 𝑩)
Page | 129
Truth tables
A truth table is used to show the output of a logic gate or circuit for all possible combinations of
input values; we usually use the binary values, 1 and 0, as shorthand for True and False.

The truth table for a two-input gate needs four rows.

INPUT OR AND NAND NOR XOR
A B
𝑿=
𝑿=𝑨+𝑩 𝑿=𝑨.𝑩 𝑿=𝑨. 𝑩 𝑿=𝑨+ 𝑩
(𝑨 . 𝑩) + (𝑨 . 𝑩)
0 0 0 0 1 1 0
0 1 1 0 1 0 1
1 0 1 0 1 0 1
1 1 1 1 0 0 0

Logic circuits

Two or more logic gates can be connected to produce a logic circuit with one or more outputs from
two or more inputs. A logic circuit can process logical expressions and binary numbers.
When producing a truth table for a logic circuit:
• it is helpful to add a column for each intermediate output as well as for the final output
• as for a single logic gate with two inputs, a logic circuit with two inputs needs four rows.
Combinational logic circuits with three inputs
We only need to be able to produce a truth table for a logic circuit with a maximum of three inputs
and six gates.
The truth table for a three-input logic circuit needs eight rows.

Designing simple logic circuits

Sometimes, it is cheaper to design and hard-wire a logic circuit for a simple automated system that
only requires a fixed pattern of output depending on the current values of the inputs, than to
program a microcontroller or computer.
We can use the words AND, OR, NOT, NAND and NAND as operators in a logical equation, such
as L = (A AND B) OR NOT B. We use brackets to indicate that the logical operation within the
brackets takes priority.
We can design a logic circuit to solve a written statement of a logical problem. First, we rewrite the
statement using brackets to clarify the binary value of each variable and the priority of the logical
operations. Then we can write the logical equation. From the logical equation, if not an earlier
stage in the rewriting process, it should be possible to draw the required logic circuit and a truth
table to confirm that it has the required behaviour.

Testing logic circuits

We have seen how to use a truth table to check whether a logic circuit has solved a given
problem, rather as we use a trace table for dry running a flowchart or pseudo code algorithm. We
can also check that a logic circuit solves the problem by building the circuit using logic simulation
software or electronic circuitry, with appropriate attention to safety.
Page | 130
Logic Building Block

It is possible to build up any logic gate, using NAND or NOR gates only.
NAND and NOR Gates can be used to build any other gates, and called „logic building block‟. It is
cost effective for manufacturer to use a single gate to build any logic circuit.
For example, the AND, OR and NOT gates can be built from these gates as shown below:
NAND as NOT:
If single input is given to NAND or NOT gate output will inverted

NAND as AND:
NAND on NAND will become AND

NAND as OR:

NAND as NOR

NAND as XOR
Page | 131
For example

Re-draw the logic circuit shown opposite, using

NAND and NOR gates only.

Complete the truth table for following circuits:

A B Working X
0 0
0 1
1 0
1 1

Which single gate performs the same function? ………………………….

A B Working X
0 0
0 1
1 0
1 1

Which single gate performs the same function? ………………………….

Page | 132
Practice Questions
Q 1) Complete the following truth table

INPUT 1 INPUT 2 OUTPUT

0 0
0 1
1 0
1 1

INPUT 1 INPUT 2 OUTPUT

0 0
0 1
1 0
1 1

Q 2) Draw the logic circuit required to fulfil the following statements:

a Output C = (NOT(A AND B)) AND (A OR B)

b Light (L) is on if Switch A is on OR (Switch B is on AND Input C is off.

Q 3)Copy and complete the truth tables for the following logic circuits:

INPUT Workspace OUTPUT

A B C
0 0
0 1
1 0
1 1
Page | 133

INPUT Workspace OUTPUT

A B C
0 0
0 1
1 0
1 1

A B C Working D
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Q 4) Three digital sensors A, B and C are used to monitor a process. The outputs from the
sensors are used as the inputs to a logic circuit.
A signal, X, is output from the logic circuit:

Output, X, has a value of 1 if either of the following two conditions occur:

• sensor A outputs the value 1 OR sensor B outputs the value 0
• sensor B outputs the value 1 AND sensor C outputs the value 0
Draw a logic circuit to represent these conditions.

A B C Working X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
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Q 5) Write a logic statement that describes the following logic circuit.

............................................................................................................................................................
..................................................................................................................................................... [3]

Q 6) The following three logic statements define the light sequence:

• R = 1 IF (A is NOT 1)
• G = 1 IF (B is 1 AND C is 1)
• Y = 1 IF (A is 1 AND NOT (B is 1 AND C is 1))
Draw the logic circuit that directly combines ALL three of these logic statements and
produces three outputs R, G and Y. [5]
Page | 135
Q 7) Four sensors (numbered 1 to 4) produce binary output which controls the lights at a rock
concert. The diagram shows how the sensors are connected:

Complete the truth table for this logic circuit. [4]

inputs outputs
sensor sensor sensor sensor
A B C
1 2 3 4
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
1 0 1 1
1 1 0 0
1 1 0 1
1 1 1 0
1 1 1 1

Q 8) Complete the truth table for the following logic circuit:

A B C X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0
Page | 136
Q 9) Complete the truth table for the following logic circuit:

A B C X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

Q 10) Complete the truth table for the following logic circuit: A B C X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

A B C X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

Simplification Logic Circuit:

Simplification means reducing the number of components in a logic circuit. As a result of
simplification the cost of production can be less. This can also improve reliability and make it
easier to trace faults if they occur.
Page | 137
Quick Revision Questions
Q 3.1) Identify each of the following gates from truth table:
INPUT 1 INPUT 2 OUTPUT INPUT 1 INPUT 2 OUTPUT
0 0 0 0 0 1
0 1 1 0 1 1
1 0 1 1 0 1
1 1 1 1 1 0

……………………………. ………………………………….
INPUT 1 INPUT 2 OUTPUT INPUT 1 INPUT 2 OUTPUT
0 0 0 0 0 o
0 1 0 0 1 1
1 0 0 1 0 1
1 1 1 1 1 0

……………………………………. ……………………………………
INPUT 1 INPUT 2 OUTPUT INPUT 2 OUTPUT
0 0 1 0 1
0 1 0 1 0
1 0 0
1 1 0

……………………………………. ……………………………………
Q 3.2) Summer 2015 P11
3 (a) Complete the truth table for the following logic circuit:

A B C Workspace X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0
Page | 138
(b) Write the Boolean statement for the following logic statement:
X = 1 if ((A is NOT 1 OR B is 1) AND C is 1) OR (B is NOT 1 AND C is 1)

……………………………………………………………………………………………………………. [3]
(c) Draw the logic circuit for the logic statement given in part b

(d) Write a logic statement which corresponds to the following logic circuit:

............................................................................................................................................................
............................................................................................................................................................
....................................................................................................................................................[3]
Page | 139

Q 3.3) Show by drawing a truth table which single logic gate or what else has the same function as
the logic circuit drawn in
a)
INPUT Workspace OUTPUT
A B X
0 0
0 1
1 0
1 1

b)

INPUT Workspace OUTPUT

A B C
0 0
0 1
1 0
1 1

c)
INPUT Workspace OUTPUT
A B X
0 0
0 1
1 0
1 1
d)
INPUT Workspace OUTPUT
A B C
0 0
0 1
1 0
1 1
e) Explain why a single logic gate is often replaced by a logic circuit such as shown in part a, b, c
and d.
............................................................................................................................................................
............................................................................................................................................................
....................................................................................................................................................[1]
Page | 140
Q 3.4) What could replace the whole logic circuit?
INPUT Workspace
P Q R X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0
Multiple output:
Q 3.5) Multiple outputs can be obtained from a logic circuit. For example in the given logic circuit 2 outputs „S‟
and „C‟ are generated.
INPUT OUTPUT
A B S C
0 0
0 1
1 0
1 1
Page | 141
Deriving Logic Statement and Drawing Logic Circuit from Given Truth Table.
Logic statement and circuit can be derived from truth table. Following are the steps:
1. Consider the output which are „1‟
2. Find a condition of input when output is „1‟
3. Check all above conditions produce output „1‟ or not.
For example

So the logic statement will be

X=1 If (D=1 AND S=0) OR (S=1 AND T=0)
The Circuit diagram will be

Q 3.6) Write logic statement for the following truth table:

A B C OUTPUT X
1 1 1 0
1 1 0 1
1 0 1 1
1 0 0 1
0 1 1 0
0 1 0 1
0 0 1 0
0 0 0 0
Page | 142
Q 3.7a) A greenhouse control system has four input parameters (H, D, T, W) and two outputs (X,
Y).
Description of
Parameter Binary value Condition
parameter
0 Too low
H Humidity
1 Acceptable
0 Night
D Day
1 Day
0 Too high
T Temperature
1 Acceptable
0 Closed
W Windows
1 Open

The watering system turns on (X = 1) if:

either it is daytime and the temperature is too high
or the humidity is too low.

The fan turns on (Y = 1) if the temperature is too high and the windows are closed.
Draw a logic circuit to represent the greenhouse control system. [6]

(b) Complete the truth table for the logic expression: X = NOT A AND (B NAND C) [4]

A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 143
Q 3.8a) An alarm system (X) is enabled and disabled using either a switch (A) or a remote control
(B).There are two infra-red sensors (C, D) and one door pressure sensor (E).

Description of
Parameter Binary value Condition
parameter
1 Switch enabled
A Switch
0 Switch disabled
1 Remote enabled
B Remote control
0 Remote disabled
1 Activated
C Infra-red sensor
0 Not activated
1 Activated
D Infra-red sensor
0 Not activated
Door pressure 1 Activated
E
sensor 0 Not activated
The alarm sounds (X = 1) if the alarm is enabled and any one or more of the sensors is
activated.
Draw a logic circuit to represent the alarm system.

(b) Complete the truth table for the logic expression: X = A OR (B XOR C) [4]
A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 144
Draw a logic circuit corresponding to the logic statement: [3]
X = (A is ON OR B is ON BUT NOT BOTH) OR (NOT(C is ONAND A is ON))
Page | 145
Q 3.9 a) A student needs to design a logic circuit to model the requirements for membership of a
snooker club. Membership (X) depends on four criteria, as shown in the table:
Description of Binary
Parameter Condition
parameter value
1 True
A Over 18
0 False
1 True
B Recommended
0 False
1 True
C Full-time
0 False
1 True
D Retired
0 False

Membership is approved (X = 1) if the person:

• is over the age of 18 and has been recommended by a pre-existing member and
• either is working full-time or is retired, but not both.

Draw a logic circuit to represent the membership requirements.

(b) Complete the truth table for the logic expression: X = (A XOR B) AND NOT C [4]

A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 146
Topical Questions from Past Papers
Q 3.1) Summer 2015 P11
3 (a) Complete the truth table for the following logic circuit:

A B C Workspace X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0

(b) Draw a logic circuit which corresponds to the following logic statement:
X = 1 if ((A is NOT 1 OR B is 1) AND C is 1) OR (B is NOT 1 AND C is 1)
Page | 147
Q 3.2) Summer 2015 P12
6 A gas fire has a safety circuit made up of logic gates. It generates an alarm (X = 1) in response to certain
conditions.
Input Description Binary Conditions
value
1 gas pressure is correct
G gas pressure
0 gas pressure is too high
1 carbon monoxide level is correct
C carbon monoxide level
0 carbon monoxide level is too high
1 no gas leak is detected
L gas leak detection
0 gas leak is detected

The output X = 1 is generated under the following conditions:

gas pressure is correct AND carbon monoxide level is too high
OR
carbon monoxide level is correct AND gas leak is detected
(a) Draw a logic circuit for this safety system. [5]

(b) Complete the truth table for the safety system. [4]

G C L Workspace X
1 1 1
1 1 0
1 0 1
1 0 0
0 1 1
0 1 0
0 0 1
0 0 0
Page | 148
Q 3.3) Summer 2016 P11 & P13
5 A computer-controlled machine produces plastic sheets. The thickness of each sheet must be
within a certain tolerance. The sheets are kept below 50 °C as they move over rollers at 10 metres
per second.
Three parameters need to be monitored all the time.
Binary
Parameter Description Conditions
value
1 thickness of sheet in tolerance
D sheet thickness
0 thickness of sheet out of tolerance
1 roller speed = 10 metres/second
S roller speed
0 roller speed <> 10 metres/second
1 temperature < 50 °C
T temperature
0 temperature >= 50 °C
An alarm, X, will sound if:
thickness is in tolerance AND (roller speed <> 10 metres/second OR temperature >= 50 °C)
OR
roller speed = 10 metres/second AND temperature >= 50 °C
(a) Draw a logic circuit to represent the above monitoring system. [6]

(b) Complete the truth table for the monitoring system. [4]
D S T Working Space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 149
Q 3.5) Winter 2016 P12
7 (a) Complete the truth tables and name the single logic gate that could replace each logic circuit:

(i) A B Working space X

0 0
0 1
1 0
1 1

Single logic gate ............................................................................................................[3]

(ii) A B Working space X

0 0
0 1
1 0

1 1

Single logic gate ............................................................................................................[3]

(b) (i) Draw a logic circuit to represent the following logic statement:
X = 1 if (A = 1 AND B = 1) OR ( (B = NOT 1) AND C = 1) [4]

(ii) Complete the truth table for the logic statement in part (b)(i). [4]
A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 150
Examiner Report
In parts (a)(i) and (ii) many candidates could complete the truth tables correctly, but were not able to state the correct
single logic gate that the table represented.
In part (b)(i) many candidates could draw a correct logic circuit. A small number of candidates used circles to
represent a logic gate. Candidates must ensure that they use the correct logic gate symbols, and that they are drawn
clearly and accurately.
In part (b) many candidates could correctly complete the truth table.
Q 3.6) Winter 2016 P11& 13
5 Three switches, A, B and C, each send values of 0 or 1 to a logic circuit. Value X is output from
the
logic circuit.

Output X has a value of 1 depending on the following conditions:

Switch A sends value 1 AND Switch B sends value 0

OR
Switch B sends value 1 AND Switch C sends value 0
(a) Draw a logic circuit to represent the conditions above.

(b) Complete the truth table for the conditions given at the start of question 5. [4]
A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 151
Examiner Report
In part (a) many candidates could draw a correct logic circuit. A small number of candidates used circles to represent a
logic gate. Candidates must ensure that they use the correct logic gate symbols, and that they are drawn clearly and
accurately.
In part (b) many candidates could correctly complete the truth table.

Q 3.7) March 2017 India

2 The diagram below shows five logic gate symbols and five names.
Draw a line between each logic gate symbol and its correct name.

Examiner Report
Nearly all candidates correctly identified the five logic gates shown.
Page | 152
Q 3.10) Summer 2017 P12
10 For this logic statement:
X = 1 if (( A is 1 AND B is 1 ) OR ( B is 1 AND C is NOT 1 ))
(a) Draw the logic circuit.

(b) Complete the truth table for the given logic statement. [4]
A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1

Examiner Comment on Q 10(a)

Many candidates provided a correct logic circuit.
Examiner Comment on Q 10(b)
Many candidates provided a correct truth table.
Page | 153
Q 3.11) Winter 2017 P12
7 Draw a logic circuit to represent the logic statement: [7]
X = 1 if (A is NOT 1 AND B is 1) AND (A is NOT 1 AND C is NOT 1) OR (B is 1 AND C is 1)

Q 3.12) Winter 2017 P13

5 (a) Draw a logic circuit for the logic statement:
X = 1 if ((A is 1 AND B is 1) OR (A is NOT 1 AND C is 1)) [4]
Page | 154
(b) Draw the symbol for an XOR gate and explain the function of this logic gate.

Explanation ........................................................................................................................
............................................................................................................................................
............................................................................................................................................
..................................................................................................................................... [5]

Q 3.13) March 2018 P12 (India)

7 (a) For this logic circuit:

Complete the truth table. [4]

A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 155
Q 3.17) Winter 2018 P12
3 A greenhouse uses a system to monitor the conditions that plants need to grow.
The inputs to the system are:
Input Binary value Condition
1 Window is open
W
0 Window is closed
1 Temperature >=26°C
T
0 Temperature <26°C
1 Humidity >=50%
H
0 Humidity <50%
The system will sound an alarm when certain conditions are detected.
Alarm (X) will sound (=1) when:
window is closed and temperature >=26°C
or
temperature <26°C and humidity >=50%
Draw a logic circuit to represent the system.

[5]
Page | 156
Q 3.18) Winter 2018 P13
10 A logic circuit is shown:

(a) Complete the truth table for the given logic circuit. [4]
A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
(b) Draw a logic circuit corresponding to the logic statement:
X = 1 if ((A is 1 AND B is 1) AND (A is 1 OR C is NOT 1)) OR (B is 1 AND C is NOT 1)

[6]
Page | 157
Q 3.19) March 2019 P12
5 Consider the following logic statement:

X = 1 if ((A is 1 NAND C is 1) NOR A is NOT 1) OR (B is 1 AND C is NOT 1)

(a) Draw a logic circuit that represents the given logic statement. Your logic gates must have a
maximum of two inputs. Do not simplify the logic statement. [6]

(b) Complete the truth table for the given logic statement. [4]

A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 158
Q 3.20) Summer 2019 P11
2 Rajesh creates a logic circuit.
He uses three different logic gates in his circuit. Each logic gate has a maximum of two inputs.
He describes the logic of each gate.
(a) “The only time the output will be 1 is when both inputs are 1.”
State the single logic gate ...................................................
Draw the single logic gate: [2]

(b) “The only time the output will be 1 is when both inputs are 0.”
State the single logic gate ...................................................
Draw the single logic gate: [2]

(c) “The only time the output will be 0 is when both inputs are 1.”
State the single logic gate ...................................................
Draw the single logic gate: [2]
Page | 159
Q 3.21) Summer 2019 P12
8 Consider the logic statement:
X = 1 if ((A is 1 NOR C is 1) AND (B is NOT 1 NOR C is 1)) OR (A is 1 AND B is 1)
(a) Draw a logic circuit to match the given logic statement. Each logic gate used must have a
maximum of two inputs. Do not attempt to simplify the logic statement.

[6]
(b) Complete the truth table for the given logic statement. [4]

A B C Working space X
0 0 0
0 0 1
0 1 0
0 1 1
1 0 0
1 0 1
1 1 0
1 1 1
Page | 160
Page | 161
Marking Scheme

Q 3.1) Summer 2015 P11

Q 3.3) Summer 2016 P11 & P13

Q 3.2) Summer 2015 P12

Page | 162

Q 3.5) Winter 2016 P12

Q 3.4) Summer 2016 P12
Page | 163

Q 3.6) Winter 2016 P11 & 13

Q 3.7) March 2017 India

Q 3.8) March 2017 India

Page | 164

Q 3.11) Winter 2017 P12

Q 3.12) Winter 2017 P13

Q 3.9) Summer 2017 P11

Q 3.10) Summer 2017 P12

Q 3.13) March 2018 P12 (India)

Page | 165
Q 3.16) Summer 2018 P12

Q 3.15) Summer 2018 P11

Q 3.17) Winter 2018 P12

Q 3.18) Winter 2018 P13

Page | 166
Q 3.19) March 2019 P12

Q 3.20) Summer 2019 P11

Page | 167
Q 3.21) Summer 2019 P12