"I never was, never have been and never will be a mathematician. I did not even know there was any system of numbers other than the scale of ten..."Today, because of the widespread nature of computers, many people are aware of the binary number representation as an alternative to decimal. This has not always been the case, as is obvious from the above quote from Freddie Williams.
F C Williams, 12th November 1974
The decimal representation of the number fifty is 50. This is a positional notation and is an abbreviation for
5x10**1 + 0x10**0(**x represents a superscripted number, eg 5x10**1 is 5x10¹)
Each digit in a number is multiplied by the number base -10 in the conventional case- raised to the power of its position, where the right most position (the units column) is taken to be 0, the next 1 (the tens), the next 2 (the hundreds) and so on. Another example, with four digits rather than just two is 1948
1x10**3 + 9x10**2 + 4x10**1 + 8x10**0Binary representation of a number employs only two digits -0 and 1- and, as might be expected the positional base is 2. The number 50 may be represented in binary as 110010. To check, just use the positional longhand form
1x2**5 + 1x2**4 + 0x2**3 + 0x2**2 + 1x2**1 + 0x2**0This is just ((2x2x2x2x2) + (2x2x2x2) + (0) + (0) + (2) + (0)), which is 32 + 16 + 0 + 0 +2, or 50.
Like all modern day computers, the Mark I stored numbers and instructions in the binary format.
Whilst binary seems completely synonymous with the on-off states of electronic circuits, it is not a necessary part of an electronic digital computer. Several early machines, such as ENIAC, were actually decimal computers.