Q.5. In which number system, alphabets like A, B, C, D, E & F are used?
Answers
Answer:
Why does the hexadecimal number system use ABCDEF?
There are only ten numeric digits, so once you get beyond base 10, you need some additional symbols to represent hexadecimal (base 16) digits that have a decimal value between 10 and 15. This is not unique to the hexadecimal number system. In base 11, you need one more symbol, in base 13, you need three more symbols. And in base 16, hexadecimal, you need six more symbols. You’ve got to get those six extra symbols from somewhere.
The use of A through F to represent the hexadecimal equivalents of the decimal values 10 through 15 has not always been used in the world of computing.
Since the early 1950s, there have been several different representations for these digits, at various times on various computer systems:
The digits 0, 1, 2, 3, 4, and 5 with lines over them were sometimes used as the hexadecimal representations of the decimal values 10 through 15, especially when expressing hexadecimal values in writing in the early 1950s.
The lowercase letters u, v, w, x, y, and z, the uppercase letters K, S, N, J, F, and L, the uppercase letters F, G, J, K, Q, and W, or the letters b, c, d, e, f, and g (so close!), in uppercase or lowercase, were sometimes used.
The letters S, T, U, V, W, and X, the letters D, G, H, J, K, and V, or the letters L, C, A, S, M, and D were sometimes used.
Sometimes, symbols that did not appear on any keyboard (then or now) were used. For example, Bruce Martin stated that the use of the letters A through F for hexadecimal digits was a “ridiculous choice” (Communications of the ACM, 10/1968, Letters to the Editor: On Binary Notation), and instead proposed the following 16 symbols for hexadecimal (and octal) notation:
If you know binary (base 2), and you tilt your head 90 degrees to the left, the notation actually makes sense. But this notation never caught on.
Like VHS winning the war with Betamax, the use of A through F (and a through f) for the additional hexadecimal digits won out over time. By the time I was writing assembly language code in 1978, hexadecimal was well-entrenched. Letters were relatively easy to remember and were convenient to type and display. And the assignment of sequential letters starting with A made counting simple, as long as you remember the first line of the .