Computer Architecture: CPU and Two's Complement

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

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.
Method 2:
- Start at -128 and work your way back to the correct negative number.
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

The central processing unit (CPU) uses main and cache memory to improve system performance.
Peripherals use interfaces to communicate with a connected device and the computer system.

Two's Complement

Two's complement is a method used to represent and handle negative numbers in binary.
There are two methods for figuring out how a negative number is stored using two's complement.
- 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.
- 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.
The range of numbers that can be stored using 8 bit Two's complement is -128 to 127.
Typically, binary is categorized in groups of 8 bits (or 1 byte).

Range for Two's Complement

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

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.