CCEA A-Level Digital Technology 2650
Systems Analysis and Development Approaches
Design, Development and Testing
Implementation and System Security
Programming
Data, Information and Data Representation
Computer Architecture and Processing Systems
System Software, Application Software and the User Interface
Web Technology and Multimedia
Networks
Databases
Artificial Intelligence, Expert Systems and Robotics
Mobile Technology, Data Mining and Cloud Computing
Individual, Social and Legal Considerations
The Development Project: Analysis and Design
The Development Project: Build, Testing and Evaluation
Data, Information and Data Representation
Two's complement and negative numbers
- 3 things to know
- AS Unit 2
Overview
Why a sign bit alone is not enough, forming a negative value by inverting and adding one, reading a negative pattern back, the range from −128 to 127, and adding a negative to a positive.
What you need to know
Answer each one before you reveal it.
In an 8-bit two's complement number, what does the leftmost bit tell you?
What range of values can 8-bit two's complement represent?
Questions from this subtopic
Each one with the model answer underneath.
- 1
Why is a special system needed to hold negative numbers in binary?
Model answer
A plain binary pattern carries no minus sign, so an agreed convention is needed that lets the same eight bits stand for negative values as well as positive ones.
- 2
In an 8-bit two's complement number, what does the leftmost bit tell you?
Model answer
The leftmost bit is the sign bit, and a 0 there means the number is positive or zero while a 1 means it is negative.
- 3
What range of values can 8-bit two's complement represent?
Model answer
Eight-bit two's complement represents every whole number from −128 to +127.
- 4
Why does the range reach one further below zero than above it?
Model answer
The pattern of all zeros is used for zero itself, which leaves 127 patterns for positive values and 128 patterns for negative ones.
- 5
Describe the procedure for writing a negative number in 8-bit two's complement.
Model answer
The size of the number is written as an 8-bit positive binary value, every bit is then inverted, and 1 is added to the inverted pattern.
- 6
What is −5 in 8-bit two's complement?
Model answer
The value −5 is 11111011, found by writing 5 as 00000101, inverting that to 11111010 and adding 1.
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