An integrated circuit, consisting of many electrical components – resistors, capacitors, transistors, logic gates... - on the same piece of semiconductor wafer is known as a microprocessor. Microprocessor is used is many electrical devices – there are many of them in computers and modern televisions, but they also appear in devices as simple as toasters.
The logic circuits that make up the microprocessor have two states (or outputs) – on and off (or 1 and 0). The inputs also consist of a series of pulses of on and off electrical signals (or 1's and 0's). The logic circuits will take the inputs, using them as instructions and produce corresponding outputs. The 1's and 0's are basically a number in binary arithmetic (base 2). Because of this on – off 1 – 0 correspondence, we can use logic circuits to perform operations on binary numbers – adding, multiplying, dividing and subtracting, or make logical decisions (if A and B, do C for example).
In fact there is a natural correspondence between numbers in base 2, base 4, base 8, and base for any positive value of n, because the place values in base 2 are as in the table below:
In fact hexadecimal, baseis commonly used in microprocessors. This allows numbers to be written much more compactly by grouping the digits in 4's, finding the decimal number of each group and converting to hexadecimal. 1110101 in base 2 is writtenso
Of course strings of digits representing binary or hexadecimal numbers would be difficult for humans to work with, so we use instead 'programming languages' such as 'C' or 'Fortran'. Programs written in these languages are decoded by microprocessors into hexadecimal which can be understood microprocessors.