15. OCR GCSE (J277) 1.2 Converting between denary & 8 bit binary

Summary

This video explains how computers store numbers using binary (base-2) and how to convert between binary and denary (base-10) systems. It introduces the concept of binary, where only 0s and 1s are used, and compares it to the denary system, which uses digits 0-9. The video walks through two methods for converting denary to binary: the divide-by-two method and the binary number line method. An example using the number 89 illustrates both methods, showing how to represent numbers in 8-bit binary format. It also covers converting binary back to denary, providing clear examples and tips for exams.

Takeaways

• 😀 Binary numbers are used by computers to represent all data, including numbers, with only 0s and 1s.
• 😀 The denary (decimal) system uses 10 digits (0-9), while the binary system uses only 2 digits (0 and 1).
• 😀 In denary, numbers are represented using columns for powers of 10, and in binary, columns represent powers of 2.
• 😀 When converting from denary to binary, we divide the number by 2 and record the remainders.
• 😀 The divide-by-two method works by dividing the number and noting the remainder at each step, then reading the remainders bottom to top.
• 😀 The binary number line method involves subtracting values corresponding to powers of 2 from the original number, writing 1s where applicable and 0s otherwise.
• 😀 The number 89 can be represented in binary as 01011001 after applying the binary number line method.
• 😀 In exams, ensure you represent numbers in the required number of bits (often 8 bits), adding leading 0s if necessary.
• 😀 To convert binary back to denary, simply add the values of the columns with 1s from the binary number line.
• 😀 For example, the binary number 01100110 converts to 102 in denary by adding 64 + 32 + 4 + 2.
• 😀 It's important to show your working in exams to minimize errors and ensure accurate results.

Q & A

What is the primary way computers store numbers?

Computers store numbers using binary, which is a system based on two states: 0s and 1s.

How does the denary number system differ from binary?

The denary system (base-10) uses ten digits (0-9) for representation, while binary (base-2) uses only two digits: 0 and 1.

How does the denary system work when we exceed 9?

When we reach 10, we introduce a new column to represent the value, using a 1 and a 0 (10), and this continues for larger numbers.

Why does binary require new columns for numbers greater than 1?

In binary, there's no number above 1, so when we need to represent a number greater than 1, we introduce new columns for each power of 2.

What is the method called for converting denary to binary?

The divide-by-two method is used to convert denary to binary, where a number is divided by 2 repeatedly, recording the remainders.

How do you read the binary number when using the divide-by-two method?

You read the binary number by starting from the last remainder and moving upwards, from bottom to top.

How do you convert denary to binary using a number line?

To convert denary to binary using a number line, write out the powers of 2, compare each power with the denary number, and subtract it if it fits, marking the corresponding column with a 1.

How do you confirm the correctness of a binary conversion?

You can confirm the correctness of a binary conversion by adding up the values of the columns where there's a 1, and ensuring the sum matches the original denary number.

What should you do if asked to provide an 8-bit binary number in an exam?

If asked for an 8-bit binary number, make sure to include all 8 bits, padding with leading zeros if necessary.

What is the maximum expected binary number conversion in GCSE exams?

In GCSE exams, you will only be expected to convert 8-bit binary numbers, which correspond to denary numbers from 0 to 255.