Question

1. Write the syntax definitions of the following objects: (a) Natural number (1, 2, 3, …)

(b) Unsigned integer (0, 1, 2, 3, …)

(c) Integer (…, -2, -1, 0, 1, 2, …)

(d) Odd number (…, -3, -1, 1, 3, …) (e) Even number (…, -4, -2, 0, 2, 4, …) (f) Integer divisible by 5 (…, -10, -5, 0, 5, 10, …)

Solve each problem from (a) to (f)using EBNF, syntax diagrams, and the parenthetic notation.

Answer 1

A) Natural Number(1,2,3,....)

<Natural number> ::= <digit exclude zero> | <Natural number> <digit>

<digit exclude zero> ::= 1|2|3|4|5|6|7|8|9

<digit> ::= 0|1|2|3|4|5|6|7|8|9

  

b) Unsigned Integer(0,1,2,3,...)

<Unsigned integer>::=<digit>|<unsigned integer><digit>

c) Integer (...., -2,-1,0,1,2,...)

<Integer> ::= <sign> <Unsigned integer>

<sign> ::= +|-|<empty>

<empty> ::=

d) Odd number (..., -3,-3,1,3, ....)

<Odd number> ::= <sign> <odd value>

<odd value> ::= <prefix><odd suffix>

<prefix> ::=<empty>|<prefix><digit>

<odd suffix>::=1|3|5|7|9

e) Even number (...,-4,-2,0,2,4, ...)

<Even number>::=<sign><even value>

<even value>::=<prefix><even suffix>

<prefix>::=<empty>|<prefix><digit>

<even suffix>::=0|2|4|6|8

f)Integer divisible by five(...,-10,-5,0,5,10,...)

<Integer divisible by five>::=<sign> <value divisible by five>

<value divisible by five>::=<prefix><suffix divisible by five>

Note:-

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