Podcast
Questions and Answers
The name of the system most commonly used to represent and handle negative numbers is '______ complement'.
The name of the system most commonly used to represent and handle negative numbers is '______ complement'.
Two's
The lowest value that can be represented with 8 bits is ______.
The lowest value that can be represented with 8 bits is ______.
-128
Typically, we categorise binary in groups of ______ bits.
Typically, we categorise binary in groups of ______ bits.
8
To calculate the binary value of a negative decimal number, one technique involves starting at ______ and working back to the answer.
To calculate the binary value of a negative decimal number, one technique involves starting at ______ and working back to the answer.
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The highest value that can be represented with 8 bits is ______.
The highest value that can be represented with 8 bits is ______.
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Data goes through the central processing unit which utilises main and ______ memory to improve system performance.
Data goes through the central processing unit which utilises main and ______ memory to improve system performance.
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Peripherals use ______ to communicate between the system and a connected device.
Peripherals use ______ to communicate between the system and a connected device.
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The overall range of 8-bit Two's complement numbers is from ______ to 127.
The overall range of 8-bit Two's complement numbers is from ______ to 127.
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The first technique to figure out how a negative number is stored using 2's complement involves starting at the right hand side of the ______.
The first technique to figure out how a negative number is stored using 2's complement involves starting at the right hand side of the ______.
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When using 8-bit Two's complement, it is necessary to include ______ numbers within the range.
When using 8-bit Two's complement, it is necessary to include ______ numbers within the range.
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Study Notes
Central Processing Unit (CPU)
- The CPU uses main and cache memory to improve system performance.
Peripherals and Interfaces
- Peripherals use interfaces to communicate between the system and connected devices.
Two's Complement for Negative Numbers
- Two's complement is the common system for representing and handling negative numbers in binary.
Calculating Two's Complement
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Method 1:
- Step 1: Add 1 to the binary representation of the positive number.
- Step 2: Start from the rightmost digit and move left.
- Step 3: Change all 1s to 0s until you reach the first 0, which becomes a 1.
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Method 2:
- Start at -128 and work your way back to the correct negative number.
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Example: -110 is represented as: 10001010
Range of Numbers in Two's Complement
- With 8-bit Two's complement, the range of numbers is -128 to 127.
- This is because one bit is used to represent the sign of the number.
Range of Numbers for Different Bit Representations
- Typically, binary is categorized in groups of 8 bits (or 1 byte).
- The range of positive and negative numbers that can be represented using 2's complement:
- 8 bits: -128 to 127
- 16 bits: -32,768 to 32,767
- 24 bits: -8,388,608 to 8,388,607
- 32 bits: -2,147,483,648 to 2,147,483,647
The CPU and Memory
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The central processing unit (CPU) uses main and cache memory to improve system performance.
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Peripherals use interfaces to communicate with a connected device and the computer system.
Two's Complement
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Two's complement is a method used to represent and handle negative numbers in binary.
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There are two methods for figuring out how a negative number is stored using two's complement.
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The first method:
- Begin at the right side of the number.
- Find the first '0' moving from right to left.
- Change the '0' to a '1'.
- Change all the '1's to the right of the '0' to '0's.
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The second method involves starting at -128 and working backwards.
- Calculate the binary value of a negative decimal number.
- For example, -110 is represented as 10001010.
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The range of numbers that can be stored using 8 bit Two's complement is -128 to 127.
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Typically, binary is categorized in groups of 8 bits (or 1 byte).
Range for Two's Complement
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The range of positive and negative numbers that can be represented using 8, 16, 24 and 32 bit 2's complement is:
- 8 bits: -128 to 127
- 16 bits: -32,768 to 32,767
- 24 bits: -8,388,608 to 8,388,607
- 32 bits: -2,147,483,648 to 2,147,483,647
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Description
This quiz covers key concepts in computer architecture, focusing on the Central Processing Unit (CPU), memory usage, and the Two's complement method for representing negative numbers in binary. Test your understanding of how peripherals interact with the system and the range of numbers in Two's complement representation.
