Fixed Point Arithmetic Dec. 2002
Presented by Fore June
Author of Windows Fan, Linux Fan

Copyrighted by Fore June, All rights reserved

Fixed-point Arithmetic

Appendix 1 Signed and Unsigned numbers relation

Unsigned value

_k-1

^k-1

₀

⁰

_-1

^-1

_-2

^-2

_-m

^-m

Obviously

U(X) = 2 x b_k x 2^k + V(X) = b_k x 2^k+1 + V(X)

^k+1

	if ( number_positive )		//  b_k = 0 
		V(X) = U(X);
	else				//number negative
		V(X) = U(X) - 2^k+1;

Example: 8-bit integer

X = 0 0 0 0 0 0 1 1
U ( X ) = 3
V ( X ) = 3

X = 1 0 0 0 0 0 1 1
U(X) = 131
V(X) = U(X) - 2⁸ = 131 - 256 = 125