78. OCR A Level (H046-H446) SLR13 - 1.4 Converting between binary, hex & denary

Summary

This video tutorial offers a comprehensive guide on converting positive integers between binary, hexadecimal, and DNA (decimal) number systems. It demonstrates the process using a table for easy reference and step-by-step examples, including converting DNA numbers like 12, 24, 230, and 100 into hexadecimal. The video also covers converting hexadecimal numbers back to binary and DNA, using nibbles (groups of four bits) to simplify the process. Key takeaways include understanding how to group binary digits into nibbles and the significance of hexadecimal letters in the conversion process.

Takeaways

• 🧬 Converting DNA numbers to hexadecimal involves first expressing the number in binary form.
• 🔢 For smaller numbers like 12, the binary is written out and grouped into 'nibbles' of four bits each to form hexadecimal.
• 🔡 The hexadecimal system uses letters (A-F) to represent values 10-15, which are crucial for larger numbers.
• 📚 The script demonstrates converting numbers like 24 and 230 to hexadecimal, emphasizing the process of grouping and translating binary nibbles.
• 🔑 It's important to note that not all DNA numbers will convert to hexadecimal numbers containing letters.
• 🔄 The process for converting from hexadecimal to binary (and then to DNA) is outlined, highlighting the reverse operation.
• 📈 For larger hexadecimal numbers like 'AB', each hexadecimal digit is converted to its 4-bit binary equivalent.
• 🔎 The script provides a method to add up the binary values to get the original DNA number.
• 📝 Examples are given for converting numbers like 100, 230, and 'AB' in hexadecimal to DNA numbers.
• 🎓 The video aims to educate viewers on how to convert between different base number systems: binary, DNA, and hexadecimal.

Q & A

What are the three base number systems discussed in the video?

The three base number systems discussed are binary (base 2), hexadecimal (base 16), and DNA (interpreted as base 10).

How do you convert the DNA number 12 to hexadecimal?

First, convert 12 to binary, which is 1100 (8 + 4 = 12). Then, split the binary into two nibbles (0000 and 1100), and convert each nibble to hex. 0000 is 0, and 1100 is 12, which is C in hex. So, the hex value of 12 is C.

Why is it useful to convert DNA numbers to hexadecimal through binary?

Converting through binary makes the process more straightforward because binary to hexadecimal conversions involve grouping bits into nibbles (groups of four), which is easier to manage when working with powers of two.

What is a nibble, and how is it used in the conversion process?

A nibble is a group of four bits. In binary to hex conversion, binary numbers are grouped into nibbles, each of which can be directly converted to a hexadecimal digit.

What is the hexadecimal representation of the DNA number 24?

First, convert 24 to binary: 11000 (16 + 8 = 24). Group the bits into two nibbles (0001 and 1000). 0001 is 1 in hex, and 1000 is 8 in hex, so 24 in DNA is 18 in hexadecimal.

How do you convert larger numbers like 230 from DNA to hexadecimal?

Convert 230 to binary: 11100110 (128 + 64 + 32 + 4 + 2 = 230). Group the bits into two nibbles (1110 and 0110). 1110 is E in hex, and 0110 is 6 in hex, so 230 in DNA is E6 in hexadecimal.

What is the importance of remembering hex digits as separate characters rather than decimal numbers?

In hexadecimal, digits represent values from 0 to 15. For example, 18 in hexadecimal is 1 and 8, not eighteen. Treating them as separate digits ensures correct conversion and avoids confusion with decimal notation.

How do you convert hexadecimal digits back to binary?

Each hexadecimal digit is converted into a 4-bit binary value. For example, A (hex) represents 10 in decimal, which is 1010 in binary. Similarly, B (hex) represents 11 in decimal, which is 1011 in binary.

What is the binary representation of the hex number 3F?

The hex digit 3 is 0011 in binary, and the digit F is 1111 in binary. Together, 3F is represented as 00111111 in binary.

How do you convert the hexadecimal digit AB to DNA?

Convert A (1010) and B (1011) to binary first. Then, sum the binary values: 10101011 in binary equals 128 + 32 + 8 + 2 + 1, which is 171 in DNA.

Outlines

00:00

🔢 Converting DNA Numbers to Hexadecimal

This paragraph explains the process of converting DNA numbers to hexadecimal format. It begins with an introduction to the conversion of positive integers between binary, hexadecimal, and DNA. The video demonstrates the conversion of the DNA number 12 to hexadecimal by first expressing it in binary (00001100), then grouping it into nibbles (groups of four bits). The leftmost nibble is '0000', which equals '0' in hexadecimal, and the rightmost nibble is '1100', which equals 'C'. Thus, 12 in DNA is '0C' or simply 'C' in hexadecimal. The paragraph also covers the conversion of the number 24 to '18' in hexadecimal and emphasizes the importance of remembering that not every DNA number will result in a hexadecimal number with letters.

05:10

🔐 Converting Large Numbers and Hexadecimal to DNA

The second paragraph delves into converting larger numbers and hexadecimal numbers back to DNA. It starts with the conversion of the number 230 in DNA to 'E6' in hexadecimal, illustrating the process of breaking down the binary representation into nibbles and translating each into its hexadecimal equivalent. The paragraph also discusses converting the number 100 in DNA to '64' in hexadecimal, highlighting the importance of correctly interpreting binary values. The video then challenges viewers to convert hexadecimal numbers 'AB' and '36' to binary and DNA, guiding them through the process of expanding each hexadecimal digit into its four-bit binary equivalent and summing the appropriate binary columns to find the DNA number. The final example involves converting '7F' from hexadecimal to DNA, which is done by breaking down '7' and 'F' into their binary components and summing the binary columns to get the DNA number. The paragraph concludes with a recap of the key question about converting between different base number systems.

Keywords

💡Binary

Binary is a base-2 number system that uses only two digits: 0 and 1. In the video, binary is used as an intermediary step when converting between decimal (DNA) and hexadecimal. For instance, the number 12 is converted into its binary form before proceeding to hexadecimal, emphasizing how binary simplifies the conversion process.

💡Hexadecimal

Hexadecimal is a base-16 number system, commonly used in computing, that includes digits 0-9 and letters A-F to represent values from 10 to 15. The video shows how to convert decimal numbers like 12 and 230 into hexadecimal (e.g., 12 becomes C in hex), and explains the role of nibbles (4 bits) in organizing binary digits for conversion into hexadecimal.

💡DNA (Decimal)

DNA, in this context, refers to the decimal or base-10 number system, which is the standard counting system using digits 0 through 9. The video illustrates how decimal numbers like 12 and 230 are converted into binary and hexadecimal. Decimal is used as the starting point for all conversions.

💡Nibbles

A nibble is a group of four binary digits, or bits, which is half a byte. The video explains that binary numbers are grouped into nibbles to simplify the conversion to hexadecimal. For example, the binary number 1100 (for decimal 12) is grouped into nibbles to be converted into the hexadecimal digit C.

💡Conversion

Conversion refers to the process of changing a number from one base system to another, such as from decimal to binary or binary to hexadecimal. The video focuses on converting between three number systems: binary, decimal (DNA), and hexadecimal. Various examples, such as converting 12, 24, and 230, demonstrate this process.

💡Bits

Bits are the fundamental units of information in binary, representing either a 0 or a 1. The video emphasizes the role of bits in binary numbers, where specific bits are grouped into nibbles to facilitate conversions to hexadecimal. For example, in the binary number 1100, each bit corresponds to a specific value in the 2's power hierarchy.

💡Base number systems

Base number systems define how many digits are used to represent numbers. The video discusses three base systems: base-2 (binary), base-10 (decimal), and base-16 (hexadecimal). Understanding these systems is essential for converting between them, as shown in the examples of converting decimal numbers like 100 into binary and hexadecimal.

💡8-bit column

The 8-bit column refers to the place value in binary for the digit representing 8 (2^3). In the video, the 8-bit column is frequently mentioned when converting binary numbers into their decimal equivalents. For instance, 1100 in binary has a 1 in the 8-bit column and a 1 in the 4-bit column, which together sum to 12 in decimal.

💡Grouping

Grouping refers to the practice of organizing binary digits into sets, such as nibbles, to make conversion to hexadecimal easier. In the video, binary numbers are grouped into nibbles of four bits, and each group is then converted into a hexadecimal digit. This concept is crucial for accurately converting between binary and hexadecimal.

💡Weightings

Weightings in binary refer to the value each bit holds based on its position, such as 1, 2, 4, 8, 16, etc. The video highlights how these weightings are used to convert between binary and decimal. For example, the binary number 1100 is analyzed using the weightings 8, 4, 2, and 1 to calculate the decimal value 12.

Highlights

Introduction to converting positive integers between binary, hexadecimal, and DNA.

Explanation of using a table for easy conversion between base number systems.

Conversion of DNA number 12 to hexadecimal by first converting to binary.

Grouping binary digits into nibbles for hexadecimal conversion.

Binary to hexadecimal conversion example with the number 12 resulting in '0c' or 'c'.

Conversion of DNA number 24 to hexadecimal, resulting in '18'.

Emphasis on the importance of using correct hexadecimal notation without letters when not applicable.

Conversion of a larger number, 230, from DNA to binary and then to hexadecimal as 'e6'.

Conversion of DNA number 100 to hexadecimal resulting in '64'.

Guidance on converting from hexadecimal to binary by first converting to DNA.

Conversion example of hexadecimal 'ab' to binary and then to DNA as 171.

Conversion of hexadecimal '36' to binary and then to DNA as 54.

Final example conversion of hexadecimal '7f' to binary and then to DNA as 127.

Summary of the video's key learning point on converting between binary, DNA, and hexadecimal.

Encouragement for viewers to practice and verify their understanding of the conversion process.

Transcripts

in this video we're going to be going

over how to convert positive integers

between binary hexadecimal and dna

[Music]

the above table allows us to easily

convert positive integers between

any of the three base number systems

that you need for the exam

base 2 to 16 10 to 16 16 to 2 and so on

and so forth

so let's have a look and converting the

dna number 12

into hexadecimal now what you want to do

is go through binary it just makes

things a lot easier

so we take the number 12 and we write it

out

in its binary which we showed you in a

previous video

so there's the number 12 in binary

naught naught naught naught

and an 8 plus a four eight plus four is

twelve

and then zero and zero at the end

now to convert this number into hex we

group our binary timeline into nibbles

so that's groups of four

so we have four zeros here well zero is

obviously zero

we don't actually need this number here

but we're showing it for completeness

and now we group the next nibble or

group of four

we have a one in the eight column and a

one

in the 4 column so 8 9 10 11

12 and remember that 12 in hex

is c so the dna number 12

in hex is 0 c

or more simply put just c

okay let's look at number 24 so first

we're going to write it out in binary

so there's number 24 it's a 16 plus an

eight

we're going to start with our left hand

nibble and notice we've got our own

mini binary waiting line of one two four

and eight

we're not using the 16 32 64 and 128

so and we have a one in the one column

so we place

one down the bottom there

we then take the next nibble and again

we have a one

in the eight column so we have eight

so the dna number 24 in hexadecimal

is one eight now that's important it's

not

18 it's one eight and it's important to

note here

that although hexadecimal has letters

available to it

not every dna number will convert into a

hexadecimal

number that contains letters

so let's look at a large number now 230.

the process is exactly the same

first of all let's write out the binary

so there's the number 230 written out in

binary

and we're going to start with the

left-hand group of four bits

the first nibble

so we have a 1 in the 8 column plus a 1

in the 4 column

plus a 1 in the 2 column so that's 8 9

10 11 12

13 14 and of course in hexadecimal

14 is e so the left nibble represents

e

in the right nibble we have a four plus

a two which is six

and in hex that is simply six so

two hundred and thirty in dna is e

six in hexadecimal

let's do one last one now of a hundred

and again

why don't you pause the video here work

through this one yourself

and then unpause the video and see if

you get the same answer we do

so first of all there's a hundred

written out in binary

now let's start with the left hand

nibble first

so we have a one and a four column and a

one in the two column

remembering again we're using the mini

binary waiting line for the nibble

not the field weightings at the top so

we've got four and a two

is six

and then the right hand nibble we just

have a one in the four column

so that's four so the dna number one

hundred

in hex is six four again remember

that's six four not sixty four

so what about if you get asked to go the

other way if you get given a hexadecimal

number

and you're asked to put it into binary

ordinary

well again if you get told to put into

dna just work through

binary first so it's quite a

straightforward process let's take a

look

so we'll start with the left hand hex

decimal digit first which is an

a and we know that needs to turn into

one nibble

so a needs to turn into four bits well a

represents

ten so that's an eight and a two so

we've got a one in the eight column

followed by

zero followed by one in the two column

followed by a zero

eight and two is ten or a in

hex we do exactly the same thing with b

the hex decimal digit b needs to turn

into

four bits or a nibble b in hex is 11

so we want an eight zero fours

and a two and a one eight nine ten

eleven

so now we have our binary equivalent

of the hex decimal digit a b

and that's one zero one zero one zero

one one

to convert that into dna we now just add

up the original binary waiting lines if

the columns have a one in

so we have 128 plus a 32 plus an eight

plus

a two plus a one is a hundred and

seventy one

so the base sixteen hex number a b

is a hundred and seventy one in dna

let's do one more let's convert the hex

decimal digit

three six that's three six not thirty

six

into binary and deanery again pause the

video

take it through binary and then unpause

and see if you've got the same answer

that we did

so you can see we've taken the three and

we've written that out there as a one in

the two column

one and the one column on the right hand

side nibble we've got

six so that's a one in the four column

and a one in the two column

we add the columns together that have

ones in 32

plus 16 plus 4 plus 2 equals

54.

let's do one final example we've got

seven f again pause the video

and see if you can work through this one

without our help

and then unpause it and see if you got

it right

so the left nibble is seven so that's

four

two and one four five six seven so

there's one in each of those columns and

a zero and the eight

and the right hand nibble is a capital f

so that is fifteen so that's all the

ones that's an

eight nine ten eleven 12 that's a 4

13 14 that's a two and one for 15.

we add together all the columns with

ones in and we end up with

and twenty seven

having watched this video you should be

able to answer the following

key question how do we convert between

the various

different base number systems binary

dna and hexadecimal

[Music]

you