Question

Give a regular expression for binary numbers. They can be integers or binary fractions. A leading - sign is always allowed. Leading 0's are not allowed except when the integer part is 0. When the binary points is present, then neither the integer part nor the fractional part are allowed to be empty. If the integer part has more than 3 bits, then grouping with commas is required. Examples: Allowed: -0 1,111,010 -1,111.00 Not allowed: .11 1000 The 4-letter alphabet consists of 0, 1, dot, and comma.

Answer 1

Solution :

We have to provide an expression for the binary numbers. There can be binary fractions or integers. Whenever there is leading 0, it is not allowed unless the integer part is a 0.

Thus the expression is :

$(-+ \in )$ $[(1+10+11+100+101+110+111)(,000+,001+,010+,011+,111+,100+,101+,110)^*$ $(\in +.(0+1)^*(0+1))+(0.(0+1)^*(0+1))]$