Number Bases / Units of Information GapFill

Number bases are simply different ways of writing numbers, the system we use in our daily lives is the decimal system (or Base 10) using the numbers 0 to 9. Computers use electronic circuits to store data and instructions and these circuits contain tiny transistors which can be in one of two states, on or off. These states can also be represented by numbers 1 or 0 and therefore are in  pixelbytesamplebinary form.

These two number bases can be compared using a table like this:

As the columns move from right to left, the previous column value is  doubleddividedcubedmultiplied by the number base, e.g. 10 x 10 = 100, 100 x 10 = 1,000 etc. and the same is true for Base 2. Binary is not just used to represent numbers, but to represent all forms of data, including  hexadecimalnumberstext, images and sounddecimal. Binary numbers are often converted to hexadecimal numbers to  represent letters as well as numbersreduce the likelihood of data becoming corruptedreduce the number of bits needed to store themmake them easier to read, as each hexadecimal digit represents four binary digits (e.g. 82 in hexadecimal is the equivalent of  1001 00011000 00101110 1101 1110 0001 in binary). Hexadecimal is a Base 16 numbering system, it uses the numbers 0 -9 and needs the additional letters  M to VA to FP to ZC and D.

Converting binary number 10100110 to decimal is achieved using a simple conversion table and completing it from the right to left:

Add all the columns with a 1 in them together to convert the number: 128 + 32 + 4 + 2 =  158166162176

Converting decimal to binary requires more stages e.g. convert 113 to binary

Step 1: 113 is smaller than 128 , insert a 0 in the column

Step 2: 113 is larger than 64, subtract 113-64 = 49. Insert a 1 in this column.

Continuing in this process the binary equivalent of 113 is  0100 00110111 00011011 00010001 0001

Converting a decimal value to a hexadecimal value requires some division, using the example of divide by 16:

113/16 = 7 remainder 1

Read the values from the hexadecimal table 113 in Base 10 =  717717111 1 in Base 16

The largest value that can be represented by the hexadecimal table above is FF which are the decimal equivalent of 255 and the binary equivalent of  1111 11111111 00011011 11001001 1001.

The fundamental unit of information in a computer system is a bit, a group of 8 bits is a byte, a kilobyte is a 1,000 bytes. The storage values increase by a power of 10 each time therefore a 1,000 megabytes is a  gigabyteterabytepetabytekilobyte and a 1,000 gigabytes is a terabyte.