17. OCR GCSE (J277) 1.2 Converting between denary and 2 digit hexadecimal

Summary

This video introduces the concept of converting between denary and two-digit hexadecimal systems. It explains how hexadecimal, a base-16 system, uses digits 0-9 and letters A-F to represent values from 0 to 15. The video delves into the relationship between binary and hexadecimal, highlighting how binary nibbles (4 bits) can easily be mapped to hexadecimal digits. The process of converting denary numbers to hexadecimal and vice versa is demonstrated through examples, helping viewers understand the practical application of hexadecimal in computer science for tasks like memory addressing and color representation.

Takeaways

• 😀 Hexadecimal is a base-16 number system, using digits 0-9 and letters A-F to represent values 10-15.
• 😀 Unlike denary (base-10) and binary (base-2), hexadecimal allows for compact representation of large binary numbers.
• 😀 Hexadecimal is commonly used in computer science for tasks such as representing colors, memory addresses, and MAC addresses.
• 😀 Converting denary to hexadecimal is made easier by first converting to binary and then grouping the binary into nibbles (4 bits).
• 😀 The Most Significant Bit (MSB) is the leftmost bit in a binary number, representing the largest value, while the Least Significant Bit (LSB) is the rightmost bit, representing the smallest value.
• 😀 The hexadecimal system uses letters A to F to represent the values 10 to 15, which simplifies the notation of larger numbers compared to using just digits.
• 😀 When converting a denary number like 12 to hexadecimal, you first convert it to binary (1100) and then group the bits into nibbles, resulting in C in hex.
• 😀 Hexadecimal numbers are written without spaces or commas, and it's important to distinguish between numbers like '18' (in decimal) and '1-8' (in hexadecimal).
• 😀 Converting hexadecimal to binary is straightforward: each hex digit corresponds to a 4-bit binary number.
• 😀 To convert hexadecimal to denary, you first convert to binary and then calculate the decimal value by adding the binary weights where there's a 1.

Q & A

What is the denary (decimal) number system?

The denary system is a base-10 system that uses the symbols 0 through 9. In this system, when we reach 10, we represent it as 1 and 0.

How does the binary system differ from the denary system?

The binary system is a base-2 system, using only the digits 0 and 1. Each place value in binary doubles as you move left, unlike the decimal system which increases by powers of 10.

What is hexadecimal and why is it used?

Hexadecimal is a base-16 system that uses digits 0 through 9 and the letters A through F to represent values from 0 to 15. It is often used in computing to represent large binary numbers in a more compact form, especially in areas like memory addresses and color codes.

Why do we use letters A to F in hexadecimal?

Since hexadecimal represents values from 0 to 15, and the numbers 10 to 15 do not have single-digit symbols in our usual numbering system, we use the letters A to F to represent these values: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

What is the relationship between binary and hexadecimal?

Each hexadecimal digit corresponds directly to a 4-bit binary 'nibble'. This close relationship makes hexadecimal a convenient shorthand for representing binary numbers.

How do you convert a denary number into hexadecimal?

To convert a denary number into hexadecimal, you first convert it to binary. Then, group the binary digits into nibbles (groups of 4). Each nibble is then converted to its hexadecimal equivalent.

What does MSB and LSB stand for in binary representation?

MSB stands for 'Most Significant Bit', which is the left-most bit in a binary number and represents the largest value. LSB stands for 'Least Significant Bit', which is the right-most bit and represents the smallest value.

How do you convert the denary number 12 to hexadecimal?

First, write 12 in binary as '1100'. Then, group the binary number into nibbles. The binary '1100' is equivalent to 'C' in hexadecimal, so 12 in denary is represented as 'C' in hexadecimal.

Why is it important to differentiate between hexadecimal numbers like '18' and '1-8'?

In hexadecimal, '18' means the value 1 and 8, whereas '1-8' means the number 1 followed by 8. This distinction helps avoid confusion between the hexadecimal number and a possible two-digit decimal number.

What steps are involved in converting a hexadecimal number to denary?

To convert a hexadecimal number to denary, convert each hexadecimal digit into its 4-bit binary equivalent, then calculate the decimal value by adding the values of the binary columns that contain 1s.

What is the denary equivalent of the hexadecimal number '7F'?

The hexadecimal '7F' is broken down into two nibbles: '7' (0111) and 'F' (1111). Adding the decimal values of the 1s in each column (64 + 32 + 16 + 8 + 4 + 2 + 1) gives 127 in denary.