### Post by noodlesoup on May 5, 2012 3:09:11 GMT

www.drpaulcarter.com/pcasm/

This is a good source. Relevant info is in part 6. I will try making this in DCPU-16, then post it later. If you beat me, go ahead and post.

Wikipedia making it incredibly easy:

"Floating-point representation is similar in concept to scientific notation. Logically, a floating-point number consists of:

A signed digit string of a given length in a given base (or radix). This digit string is referred to as the significand, coefficient or, less often, the mantissa (see below). The length of the significand determines the precision to which numbers can be represented. The radix point position is assumed to always be somewhere within the significand—often just after or just before the most significant digit, or to the right of the rightmost (least significant) digit. This article will generally follow the convention that the radix point is just after the most significant (leftmost) digit.

A signed integer exponent, also referred to as the characteristic or scale, which modifies the magnitude of the number.

To derive the value of the floating point number, one must multiply the significand by the base raised to the power of the exponent, equivalent to shifting the radix point from its implied position by a number of places equal to the value of the exponent—to the right if the exponent is positive or to the left if the exponent is negative.

Using base-10 (the familiar decimal notation) as an example, the number 152853.5047, which has ten decimal digits of precision, is represented as the significand 1528535047 together with an exponent of 5 (if the implied position of the radix point is after the first most significant digit, here 1). To determine the actual value, a decimal point is placed after the first digit of the significand and the result is multiplied by 105 to give 1.528535047 × 105, or 152853.5047. In storing such a number, the base (10) need not be stored, since it will be the same for the entire range of supported numbers, and can thus be inferred.

Symbolically, this final value is

s times b^e "

This is a good source. Relevant info is in part 6. I will try making this in DCPU-16, then post it later. If you beat me, go ahead and post.

Wikipedia making it incredibly easy:

"Floating-point representation is similar in concept to scientific notation. Logically, a floating-point number consists of:

A signed digit string of a given length in a given base (or radix). This digit string is referred to as the significand, coefficient or, less often, the mantissa (see below). The length of the significand determines the precision to which numbers can be represented. The radix point position is assumed to always be somewhere within the significand—often just after or just before the most significant digit, or to the right of the rightmost (least significant) digit. This article will generally follow the convention that the radix point is just after the most significant (leftmost) digit.

A signed integer exponent, also referred to as the characteristic or scale, which modifies the magnitude of the number.

To derive the value of the floating point number, one must multiply the significand by the base raised to the power of the exponent, equivalent to shifting the radix point from its implied position by a number of places equal to the value of the exponent—to the right if the exponent is positive or to the left if the exponent is negative.

Using base-10 (the familiar decimal notation) as an example, the number 152853.5047, which has ten decimal digits of precision, is represented as the significand 1528535047 together with an exponent of 5 (if the implied position of the radix point is after the first most significant digit, here 1). To determine the actual value, a decimal point is placed after the first digit of the significand and the result is multiplied by 105 to give 1.528535047 × 105, or 152853.5047. In storing such a number, the base (10) need not be stored, since it will be the same for the entire range of supported numbers, and can thus be inferred.

Symbolically, this final value is

s times b^e "