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The \d can be used to match single number. Alternatively the [0-9] can be used to match single number in a regular expression. The [0-9] means between 0 and 9 a single number can match.
In this case, [0-9]+ matches one or more digits. A regex may match a portion of the input (i.e., substring) or the entire input. In fact, it could match zero or more substrings of the input (with global modifier). This regex matches any numeric substring (of digits 0 to 9) of the input.
The regex [0-9] matches single-digit numbers 0 to 9. [1-9][0-9] matches double-digit numbers 10 to 99. That's the easy part. Matching the three-digit numbers is a little more complicated, since we need to exclude numbers 256 through 999.
Basically (0+1)* mathes any sequence of ones and zeroes. So, in your example (0+1)*1(0+1)* should match any sequence that has 1. It would not match 000 , but it would match 010 , 1 , 111 etc. (0+1) means 0 OR 1.
Your regex ^[0-9] matches anything beginning with a digit, including strings like "1A". To avoid a partial match, append a $ to the end:
^[0-9]*$
This accepts any number of digits, including none. To accept one or more digits, change the * to +. To accept exactly one digit, just remove the *.
UPDATE: You mixed up the arguments to IsMatch. The pattern should be the second argument, not the first:
if (!System.Text.RegularExpressions.Regex.IsMatch(textbox.Text, "^[0-9]*$"))
CAUTION: In JavaScript, \d is equivalent to [0-9], but in .NET, \d by default matches any Unicode decimal digit, including exotic fare like ႒ (Myanmar 2) and ߉ (N'Ko 9). Unless your app is prepared to deal with these characters, stick with [0-9] (or supply the RegexOptions.ECMAScript flag).
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