Notation of bits in C

Question

I'm reading "The C Programming Language" and in the section on bitwise operations they write things like:

x & ~077

What do the 7s in 077 stand for?

Answer 1

In C, any number literal beginning with "0" and followed by digits between 0 and 7 (inclusive) is a value in octal notation. That is, the numeral base if 8.

So the number "077" has the decimal value of:

• 0 * 8²
• + 7 * 8¹
• + 7 * 8?
• = 0 + 56 + 7
• = 63

Or, as binary value with leading zeroes: "000111111".

The octal system was in wider use in former CS times, before the hex(adecimal) system took over. Both of these numeral systems have the advantage that each digit represents a set of bits. An octal digit stands for 3 bits, and a hex digit stands for 4 bits. A value in decimal notation cannot be "translated" simply digit-by-digit.

This is not the place to teach you the basics of number systems, you might want to read the Wikipedia page on positional notation to start with learning.