Integers

[AJ87]

Hi guys

As a total amateur with programming I’ve started learning from ‘Herbert Schildt C++ A Beginner’s Guide’ and up till now I’ve been fine with it, but now it’s gone into more detail with Integers and I just can’t get my head around what the author is saying in this one paragraph:

‘Signed integers are important for a great many algorithms, but they have only half the absolute magnitude of their unsigned relatives. For example, assuming a 16-bit integer, here is 32,767:

01111111 11111111

For a signed value, if the high-order bit were set to 1, the number would then be interpreted as -1 (assuming the two’s complement format). However, if you declared this to be an unsigned int, then when the high-order bit was set to 1, the number would become 65,535.’

What the hell is with the ‘0’s’ and ‘1’s’ and how do they become 32,767 ???

I know to most of you this is probably a stupid question, but if somebody could spare a moment to explain it in simple English I’d really appreciate it.

Many thanks

[Chervil]

That's binary numbers for you. Internally, the only thing the computer understands is "off" and "on". Those two states represent the digit 0 and 1.

A decimal number such as 1234 can be understood as

  1 * 1000 
+ 2 * 100
+ 3 * 10
+ 4 * 1

For a binary numbers things are similar but instead of powers of 10 we use powers of 2.
so the binary number 11011010 can be understood as

  1 * 128
+ 1 * 64
+ 0 * 32
+ 1 * 16
+ 1 * 8
+ 0 * 4
+ 1 * 2
+ 0 * 1

which gives the decimal value 218.

There's a very simple binary-decimal converter on this page http://www.mathsisfun.com/binary-decimal-hexadecimal-converter.html

If you need more, google "binary numbers".

[AJ87]

That's great, thanks for that, I think I get it now.