ECAP268 - U01L04 - Fixed point and floating point representation

Summary

This lecture delves into the representation of integers in computers, focusing on fixed and floating point representations. It explains how positive and negative integers are encoded using bits, with the sign bit determining the value's positivity or negativity. The video introduces three methods for representing negative numbers: sign magnitude, one's complement, and two's complement. It also covers the concept of mantissa and exponent in floating point representation, demonstrating how to encode numbers like 6132.789 as a combination of a fixed point number and an exponent.

Takeaways

• 🖥️ Computers represent integers using binary numbers, with different methods for positive and negative values.
• 🔢 Positive integers and zero are represented as unsigned numbers, while negative integers require a notation to denote their sign.
• 🔣 In computer systems, the sign of an integer is represented by a bit in the leftmost position, with '0' for positive and '1' for negative.
• 📍 The position of the decimal or binary point is crucial for representing fractions, integers, or mixed numbers in computers.
• 🔁 There are two main types of fixed point representation: one with the binary point fixed at the leftmost position (fraction) and the other at the rightmost position (integer).
• 🔑 The sign of a positive integer is represented by a '0', and its magnitude by a positive binary number.
• 📌 Negative integers can be represented in three ways: sign-magnitude, one's complement, and two's complement.
• 🔄 In sign-magnitude representation, the sign is indicated by '1' for negative, followed by the binary representation of the number.
• 🔄 One's complement representation is found by taking the complement of the binary number representing the positive value.
• 🔄 Two's complement representation is obtained by adding one to the one's complement of the positive number.
• 🔄 Floating point representation uses two registers: one for the mantissa (fixed point number) and another for the exponent (position of the decimal point).

Q & A

What are the two main types of integer representation discussed in the lecture?

The two main types of integer representation discussed are fixed point representation and floating point representation.

How are positive integers and zero represented in computers?

Positive integers and zero are represented as unsigned numbers in computers, using only zeros and ones without any additional notation.