A system and method are provided for rational division. The method accepts accepting a binary numerator and a binary denominator. A binary first sum is created of the numerator and a binary first count from a previous cycle. A binary first difference is created between the first sum and the denominator. In response to comparing the first sum with the denominator, and first carry bit is generated and added to a first binary sequence. The first binary sequence is used to generate a k-bit quotient. Typically, the denominator value is larger than the numerator value. In one aspect, the numerator and denominator form a rational number. Alternately, the numerator may be an n-bit bit value formed as either a repeating or non-repeating sequence, and the denominator is an (n+1)-bit number with a decimal value of 2(n+1).