IB Design Technology Topic A3.4.5 Digital Signal…

Digital Systems: Everything Reduced to On or Off

Digital systems are designed to store, process, and communicate information in digital form.
They use discrete values, such as binary digits (0s and 1s), to represent data.

Note

A digital system stores, processes and communicates information using only discrete values.
Almost always those values are just two: on and off, high and low, 1 and 0.
Everything a computer does is built out of that one impoverished choice, repeated at enormous speed.

Binary Digits

Definition

Binary Digit

A binary digit has either a value of 0 or 1. These values correspond to on and off signals in electronic circuits.

Analogy

Think of binary digits like a light switch: 0 represents the switch being off, and 1 represents it being on.

Logic Gates

Definition

Logic Gates

A digital device that performs a Boolean function, controlling whether an input signal passes through to the output based on logical rules (e.g., AND, OR, NOT).

Note

Logic gates are the fundamental building blocks of digital circuits, enabling complex computations and decision-making processes.

How Logic Gates Work

Logic gates use transistors to control the flow of electricity.
Transistors act as switches, turning on or off based on the input signals.
The combination of these switches determines the gate's output.

Analogy

Consider a logic gate as a series of water pipes with valves.
The transistors are the valves, controlling the flow of water (electricity) based on the input conditions.

The Gates You Need to Know

AND Gate
1. Outputs 1 only if all inputs are 1.
2. Symbol: D-shaped with a flat side for inputs and a curved side for output.
NOT Gate
1. Inverts the input: 0 becomes 1, and 1 becomes 0.
2. Symbol: Triangle with a circle at the output.
OR Gate
1. Outputs 1 if at least one input is 1.
2. Symbol: Curved shape with a pointed output.
XOR Gate
1. Outputs 1 if exactly one input is 1.
2. Symbol: OR gate with an extra curved line on the input side.
NOR Gate
1. Outputs 1 only when both inputs are 0, so it is an OR gate with the output inverted.
2. Symbol: OR gate with a circle at the output.
XNOR Gate
1. Outputs 1 if inputs are equal.
2. Symbol: XOR gate with a circle at the output.
NAND Gate
1. Outputs 0 only when both inputs are 1, so it is an AND gate with the output inverted.
2. Symbol: an AND gate with a circle at the output. Any circle on a gate symbol means the output is inverted.

The Truth Tables

A truth table lists every possible combination of inputs and the output each one produces.
With two inputs there are only four combinations, so a two-input gate is completely described by four rows.

Input A	Input B	AND	OR	NAND	NOR	XOR	XNOR
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Notice the pattern: NAND is the exact opposite of AND, NOR is the exact opposite of OR, and XNOR is the exact opposite of XOR.
The NOT gate is the only one with a single input, and it simply flips it.

Common Mistake

OR and XOR are not the same gate.
OR outputs 1 when at least one input is 1, including when both are.
XOR outputs 1 when exactly one input is 1, and drops back to 0 when both are.
They differ in exactly one row of the truth table, and that is the row examiners test.

Tip

When analyzing logic gates, always start by identifying the type of gate and its inputs.
This will help you predict the output accurately.

What Digital Buys, and What It Costs

Advantages	Disadvantages
Noise Resistance: Binary signals are less affected by interference	Loss of Detail: Quantization can lead to a loss of subtle information
Easy Storage and Processing: Data can be compressed, encrypted, and transmitted efficiently	Complexity: Requires conversion from analogue to digital and vice versa

Example question

A logic gate outputs 1 only when both of its inputs are 1. Which gate is it? (1 mark)

A. OR

B. NOR

C. XOR

D. AND

Solution

1 mark for the correct answer: D, AND.

OR would also output 1 when only one input is 1, so it is not restrictive enough.
XOR is the trap: it outputs 1 for exactly one input, and outputs 0 when both are 1, which is the opposite of what is asked.

Example question

A microwave oven will only run when the door is closed (input A) AND the start button is pressed (input B). A signal of 1 means the condition is met.

(a) Identify the logic gate that controls the motor, and complete its truth table. (3 marks)

(b) Explain why a designer would choose this gate rather than an OR gate for this safety function. (2 marks)

Solution

(a) Award [1] for identifying the gate and [1] for each correct half of the truth table, up to [3 max].

It is an AND gate. [1]
A = 0, B = 0 gives output 0. A = 0, B = 1 gives output 0. [1]
A = 1, B = 0 gives output 0. A = 1, B = 1 gives output 1. [1]

(b) Award [1] for each point, up to [2 max].

An AND gate requires every condition to be met before it will output 1, so the oven cannot run unless the door is closed. [1]
An OR gate would output 1 if only the start button were pressed, so the microwave would run with the door open and expose the user to radiation. [1]

Active recall

What is a binary digit, and what two values can it take?
What is a logic gate, and which component actually does the switching inside one?
State the one row of the truth table where OR and XOR disagree.
What does a circle on the output of a gate symbol always mean?
Give one disadvantage of representing a real signal digitally.

Digital Systems: Everything Reduced to On or Off

Digital systems are designed to store, process, and communicate information in digital form.
They use discrete values, such as binary digits (0s and 1s), to represent data.

Note

A digital system stores, processes and communicates information using only discrete values.
Almost always those values are just two: on and off, high and low, 1 and 0.
Everything a computer does is built out of that one impoverished choice, repeated at enormous speed.

Binary Digits

Definition

Binary Digit

A binary digit has either a value of 0 or 1. These values correspond to on and off signals in electronic circuits.

Analogy

Think of binary digits like a light switch: 0 represents the switch being off, and 1 represents it being on.

Logic Gates

Definition

Logic Gates

A digital device that performs a Boolean function, controlling whether an input signal passes through to the output based on logical rules (e.g., AND, OR, NOT).

Note

Logic gates are the fundamental building blocks of digital circuits, enabling complex computations and decision-making processes.

How Logic Gates Work

Logic gates use transistors to control the flow of electricity.
Transistors act as switches, turning on or off based on the input signals.
The combination of these switches determines the gate's output.

Analogy

Consider a logic gate as a series of water pipes with valves.
The transistors are the valves, controlling the flow of water (electricity) based on the input conditions.

The Gates You Need to Know

AND Gate
1. Outputs 1 only if all inputs are 1.
2. Symbol: D-shaped with a flat side for inputs and a curved side for output.
NOT Gate
1. Inverts the input: 0 becomes 1, and 1 becomes 0.
2. Symbol: Triangle with a circle at the output.
OR Gate
1. Outputs 1 if at least one input is 1.
2. Symbol: Curved shape with a pointed output.
XOR Gate
1. Outputs 1 if exactly one input is 1.
2. Symbol: OR gate with an extra curved line on the input side.
NOR Gate
1. Outputs 1 only when both inputs are 0, so it is an OR gate with the output inverted.
2. Symbol: OR gate with a circle at the output.
XNOR Gate
1. Outputs 1 if inputs are equal.
2. Symbol: XOR gate with a circle at the output.
NAND Gate
1. Outputs 0 only when both inputs are 1, so it is an AND gate with the output inverted.
2. Symbol: an AND gate with a circle at the output. Any circle on a gate symbol means the output is inverted.

The Truth Tables

A truth table lists every possible combination of inputs and the output each one produces.
With two inputs there are only four combinations, so a two-input gate is completely described by four rows.

Input A	Input B	AND	OR	NAND	NOR	XOR	XNOR
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Notice the pattern: NAND is the exact opposite of AND, NOR is the exact opposite of OR, and XNOR is the exact opposite of XOR.
The NOT gate is the only one with a single input, and it simply flips it.

Common Mistake

OR and XOR are not the same gate.
OR outputs 1 when at least one input is 1, including when both are.
XOR outputs 1 when exactly one input is 1, and drops back to 0 when both are.
They differ in exactly one row of the truth table, and that is the row examiners test.

Tip

When analyzing logic gates, always start by identifying the type of gate and its inputs.
This will help you predict the output accurately.

What Digital Buys, and What It Costs

Advantages	Disadvantages
Noise Resistance: Binary signals are less affected by interference	Loss of Detail: Quantization can lead to a loss of subtle information
Easy Storage and Processing: Data can be compressed, encrypted, and transmitted efficiently	Complexity: Requires conversion from analogue to digital and vice versa

Example question

A logic gate outputs 1 only when both of its inputs are 1. Which gate is it? (1 mark)

A. OR

B. NOR

C. XOR

D. AND

Solution

1 mark for the correct answer: D, AND.

OR would also output 1 when only one input is 1, so it is not restrictive enough.
XOR is the trap: it outputs 1 for exactly one input, and outputs 0 when both are 1, which is the opposite of what is asked.

Example question

A microwave oven will only run when the door is closed (input A) AND the start button is pressed (input B). A signal of 1 means the condition is met.

(a) Identify the logic gate that controls the motor, and complete its truth table. (3 marks)

(b) Explain why a designer would choose this gate rather than an OR gate for this safety function. (2 marks)

Solution

(a) Award [1] for identifying the gate and [1] for each correct half of the truth table, up to [3 max].

It is an AND gate. [1]
A = 0, B = 0 gives output 0. A = 0, B = 1 gives output 0. [1]
A = 1, B = 0 gives output 0. A = 1, B = 1 gives output 1. [1]

(b) Award [1] for each point, up to [2 max].

An AND gate requires every condition to be met before it will output 1, so the oven cannot run unless the door is closed. [1]
An OR gate would output 1 if only the start button were pressed, so the microwave would run with the door open and expose the user to radiation. [1]

Active recall

What is a binary digit, and what two values can it take?
What is a logic gate, and which component actually does the switching inside one?
State the one row of the truth table where OR and XOR disagree.
What does a circle on the output of a gate symbol always mean?
Give one disadvantage of representing a real signal digitally.

IB Design Technology Topic A3.4.5: Digital Signal Systems Notes

IB Design Technology Topic A3.4.5: Digital Signal Systems Notes

Digital Systems: Everything Reduced to On or Off

Binary Digits

Logic Gates

How Logic Gates Work

The Gates You Need to Know

The Truth Tables

What Digital Buys, and What It Costs

Digital Systems: Everything Reduced to On or Off

Binary Digits

Logic Gates

How Logic Gates Work

The Gates You Need to Know

The Truth Tables

What Digital Buys, and What It Costs

A. Design in theory

B. Design in practice

C. Design in context

IB Design Technology Topic A3.4.5: Digital Signal Systems Notes

A. Design in theory

B. Design in practice

C. Design in context

IB Design Technology Topic A3.4.5: Digital Signal Systems Notes

Digital Systems: Everything Reduced to On or Off

Binary Digits

Logic Gates

How Logic Gates Work

The Gates You Need to Know

The Truth Tables

What Digital Buys, and What It Costs

Digital Systems: Everything Reduced to On or Off

Binary Digits

Logic Gates

How Logic Gates Work

The Gates You Need to Know

The Truth Tables

What Digital Buys, and What It Costs