Computer Arithmetic for Double Precision Numbers

[ver_mathstats]

Homework Statement

In double precision for what values of a does this expression evaluate to 1?

The expression is (1-a)(1+a).

Relevant Equations

(1-a)(1+a)

I know that this expression evaluates to 1 when a is equal to 0. Also for when a is equal to 1/n when n is a positive number, but I'm confused about how to go about this in double precision?

 

[berkeman]

Homework Statement:: In double precision for what values of a does this expression evaluate to 1?

The expression is (1-a)(1+a).
Relevant Equations:: (1-a)(1+a)

I know that this expression evaluates to 1 when a is equal to 0. Also for when a is equal to 1/n when n is a positive number, but I'm confused about how to go about this in double precision?

Assuming you mean Fixed Point and not Floating Point, what data representation are you supposed to use for this problem?

https://www.mathworks.com/help/fixedpoint/ug/fixed-point-data-types_btb4ld0-1.html

 

[ver_mathstats]

Assuming you mean Fixed Point and not Floating Point, what data representation are you supposed to use for this problem?

https://www.mathworks.com/help/fixedpoint/ug/fixed-point-data-types_btb4ld0-1.html

View attachment 314636

We did not learn one's complement or two's complement in this particular class, so neither of those.

 

[pbuk]

Assuming you mean Fixed Point and not Floating Point, what data representation are you supposed to use for this problem?

The problem states "double precision" which is floating point, specifically it is the binary64 implementation of IEEE754: https://en.wikipedia.org/wiki/Double-precision_floating-point_format.

@ver_mathstats can you answer the similar question "In double precision for what values of a does $1 - a$ evaluate to 1?"