74. OCR A Level (H046-H446) SLR13 - 1.4 Sign and magnitude

Summary

This video explains how negative numbers are represented in binary using the sign and magnitude method, distinguishing it from positive number representation and introducing the concept of a sign bit.

Highlights

The Challenge of Representing Negative Numbers00:00:14

Binary numbers typically increase in value when any '1' is added. This raises the question of how to represent negative numbers if adding '1' always makes a number positive.

Methods for Representing Negative Numbers00:01:04

There are two main methods for representing negative numbers in binary: sign and magnitude, and two's complement. This video focuses on the sign and magnitude method.

Sign and Magnitude Explained00:01:25

In sign and magnitude, positive numbers start with a '0' and negative numbers start with a '1'. The leftmost bit, known as the Most Significant Bit (MSB), becomes a 'sign bit' rather than contributing to the numerical value.

Impact on Binary Range00:02:32

Because the MSB is used as a sign bit, it no longer holds a weighted value. This means that for an 8-bit binary number, the largest positive number that can be stored is +127, but it also allows for the representation of negative numbers from -1 to -127.