Objectives
- To be able to define the terms, bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte.
- To understand that data needs to be converted into binary format to be processed by the computer.
Units
We looked before at binary and said that it was a base 2 system. Well just like base 10 has key values like grams and kilograms, binary has it's own names to describe key values.
The basic unit is 0 or 1. This is a binary digit or bit.
Any group of 8 bits is called a byte and half a byte (4 bits) is called a nibble (nerdy computer humour!)
We also use the kilo prefix to represent the same sort of scale as we do in base 10. But 1000 is not a very tidy binary number so we go to the closest 'tidy' value in binary which is 2 to the 10 or 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024.
Using this approximation to 1000 we can now define a whole set of names commonly used to describe binary numbers.
8 bits 1 byte
1024 bytes 1 kilobyte
1024 kilobytes 1 megabyte
1024 megabytes 1 gigabyte
1024 gigabytes 1 terabyte
The basic unit is 0 or 1. This is a binary digit or bit.
Any group of 8 bits is called a byte and half a byte (4 bits) is called a nibble (nerdy computer humour!)
We also use the kilo prefix to represent the same sort of scale as we do in base 10. But 1000 is not a very tidy binary number so we go to the closest 'tidy' value in binary which is 2 to the 10 or 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1024.
Using this approximation to 1000 we can now define a whole set of names commonly used to describe binary numbers.
8 bits 1 byte
1024 bytes 1 kilobyte
1024 kilobytes 1 megabyte
1024 megabytes 1 gigabyte
1024 gigabytes 1 terabyte
Numbers
We have already looked at the connection between binary and denary numbers. Converting binary integers into their base 10 equivalent is a relatively straightforward process. You simply write the binary number under the binary column headings and add up those columns where there is a 1.
Let's look at another example:
What is the denary (base 10) equivalent of 11011001 in binary?
Let's look at another example:
What is the denary (base 10) equivalent of 11011001 in binary?
128 + 64 +16 +8 +1 = 217
The process to convert from base 10 to binary can also be quite straightforward. There are other methods, but a simple approach is to divide by 2 repeatedly noting the remainder value each time until the answer is 0.
The process to convert from base 10 to binary can also be quite straightforward. There are other methods, but a simple approach is to divide by 2 repeatedly noting the remainder value each time until the answer is 0.
The answer is the remainder column starting at the last value.
11011001
11011001
Task
In your exercise books:
b 10001 + 11001
c 111001 + 100011
7. Extension: Can you find out what name is used for units larger than a terabyte?
- Write down a definition for each of the value descriptors of binary. (bits, bytes, etc).
- Convert the following from base 10 into binary: 28, 72, 131, 235, and 255
- Convert the following from binary to denary (base 10): 1011, 11011, 10001010 and 11001000
- How many kilobytes are in a gigabyte?
- How many megabytes are there in 3 terabytes?
- Add the following numbers in binary showing your working:
b 10001 + 11001
c 111001 + 100011
7. Extension: Can you find out what name is used for units larger than a terabyte?