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

Summary

This video explains how to represent negative numbers in binary using the 'sign and magnitude' method. The presenter first reminds viewers that in binary, the smallest number is zero, and adding any ones increases a number's value. The challenge is to represent negative numbers like -10. The video introduces two methods: 'sign and magnitude' and 'two's complement.' Focusing on the 'sign and magnitude' method, the key concept is that the leftmost bit (MSB) becomes a sign bit—0 for positive, 1 for negative—allowing representation of both positive and negative numbers, but reducing the maximum positive value from 255 to 127.

Takeaways

• 😀 The video explains how to represent negative numbers in binary using the sine and magnitude method.
• 🔢 The smallest number in binary is 0, which in an 8-bit system is represented by a sequence of zeros.
• ➕ Adding any ones to the binary sequence increases the value, resulting in positive numbers.
• ❓ The key question raised is how to represent negative numbers in binary when adding ones only increases value.
• 🧮 There are multiple methods to represent negative numbers in binary, with sine and magnitude being one of them.
• 🔑 Positive numbers always start with a 0, while negative numbers start with a 1 in the sine and magnitude method.
• 🔀 The most significant bit (MSB) becomes the sign bit, with 1 indicating negative and 0 indicating positive.
• 📉 In the sine and magnitude method, the largest positive number that can be stored in 8-bit binary is 127, and the range of negative numbers goes from -1 to -127.
• 📊 The MSB in this system no longer holds a weighted value, but only indicates the sign of the number.
• 🎯 After watching the video, you should be able to explain how to represent negative numbers in binary using the sine and magnitude method.

Q & A

What is the smallest number that can be represented in binary?

The smallest number that can be represented in binary is zero, which is a sequence of zeros in all columns.

What happens when you add ones to any column in binary?

When ones are added to any column in binary, the value of the number increases, making the number positive and increasing its magnitude.

How do we represent negative numbers in binary?

Negative numbers in binary can be represented using methods like 'sine and magnitude' or 'two's complement.' This video focuses on the sine and magnitude method.

What are the two main methods for representing negative numbers in binary?

The two main methods for representing negative numbers in binary are 'sine and magnitude' and 'two's complement.'

In the sine and magnitude method, what does the leftmost bit represent?

In the sine and magnitude method, the leftmost bit, or the most significant bit (MSB), represents the sign: '1' for a negative number and '0' for a positive number.

How does the binary representation of a positive number compare to its negative counterpart in sine and magnitude?

In sine and magnitude, the binary representation of a positive number is the same as its negative counterpart, except for the leftmost bit, which is used to indicate the sign.

What range of numbers can be represented using 8-bit binary in the sine and magnitude method?

In the sine and magnitude method using 8-bit binary, the range is from -127 to +127.

Why can't the leftmost bit be used to hold a value in sine and magnitude?

The leftmost bit in sine and magnitude is reserved for indicating the sign of the number, so it can no longer represent a value.

What is the largest positive number that can be stored in 8-bit binary using sine and magnitude?

The largest positive number that can be stored in 8-bit binary using sine and magnitude is +127.

How does using the sine and magnitude method affect the total number of positive and negative values that can be represented?

Using the sine and magnitude method reduces the number of positive values that can be represented, but allows for an equal number of negative values ranging from -1 to -127.