Przesuń dodaj !!!

11 x -11


x = 01011

y = -11 = ~(01011) + 1 = 10100 + 1 = 10101



A = 0
S = 0
M = Y = 10101
Q = X = 01011


 S |  A  |  Q  | operacja
 --+-----+-----+----------
 0 |00000|01011| Q0 = 1 -> A = M + A
 1 |10101|01011| ASR (1)
 1 |11010|10101| Q0 = 1 -> A = M + A
 1 |01111|10101| ASR (2)
 1 |10111|11010| Q0 = 0 -> ASR (3)
 1 |11011|11101| Q0 = 1 -> A = M + A
 1 |10000|11101| ASR (4)
 1 |11000|01110| ASR (5) (OSTATNI ASR, BO JEST GO TYLE CO BITÓW!)
 1 |11100|00111| KONIEC


 Z = 1110000111
 -z = ~(1110000111) + 1 = 0001111000 + 1 = 0001111001


	10101
	11010
	-----
	01111

	10101
	11011
	-----
	10000


-6 x 5


x = 6 = 00110
y = -5 = -00101 = ~(00101) + 1 = 11010 + 1 = 11011


A = 0
S = 0
M = Y = 11011
Q = X = 00110

 S |  A  |  Q  | operacja
---+-----+-----+----------
 0 |00000|00110| Q0 = 0 ASR (1)
 0 |00000|00011| Q0 = 1 -> A = A + M
 1 |11011|00011| ASR (2)
 1 |11101|10001| Q0 = 1 -> A = A + M
 1 |11000|10001| ASR (3)
 1 |11100|01000| Q0 = 0 ASR (4)
 1 |11110|00100| Q0 = 0 ASR (5)
 1 |11111|00010| KONIEC

Z = 1111100010
~(1111100010) + 1 = 0000011101 + 1 = 0000011110

-13 x -14

x = -13 = 13 = 01101
y = -14 = 14 = 01110

A = 0
S = 0
M = Y = 01110
Q = X = 01101

 S |  A  |  Q  | operacja
---+-----+-----+----------
 0 |00000|01101| Q0 = 1 -> A = A + M
 0 |01110|01101| ASR (1)
 0 |00111|00110| Q0 = 0 ASR (2)
 0 |00011|10011| Q0 = 1 -> A = A + M
 0 |10001|10011| ASR (3)
 0 |01000|11001| Q0 = 1 -> A = A + M
 0 |10110|11001| ASR (4)
 0 |01011|01100| ASR (5)
 0 |00101|10110| KONIEC

Z = 0010110110


ALGORYTM BOOTHA !!!


 -5/16 x -7/8

 X = -5/16
 Y = -7/8

 zakładamy format U2 w postaci xx.xxxx dla x,y
 wynik będzie w formacie xxxx.xxxxxxxx (suma cyfr przed i po przecinku)

 zapiszmy liczbę 5/16 na 4 bitach po przecinku

 5/16 * 2^4 = 5/16 * 16 = 5 -> 0101

 5/16 = 00.0101
 -5/16 = ~00.0101 + 0.0001 = 11.1011

 7/8 * 2^4 = 7/8 * 16 = 14 -> 1110
 -00.1110 = ~00.1110 + 1 = 11.0001 + 1 = 11.0010

 Na potrzeby wykonania algorytmu kropkę pominiemy i wstawimy ją na końcu

 A = 0 Q = Y = 11.0010 M = X = 11.1011 Q - 1 = 00

 A    | Q    |Q-1|   Operacja
--------------------------
000000|110010|0  |  (Q0,Q-1)=(0,0) więc ASR(1)
000000|011001|0  |  (Q0,Q-1)=(1,0) więc odejmujemy  A = A - M
000101|011001|0  |  ASR (2)
000010|101100|1  |  (Q0,Q-1)=(0,1) więc A = A+M
111101|101100|1  |  ASR (3)
111110|110110|0  |  (Q0,Q-1)=(0,0) więc ASR(4)
111111|011011|0  |  (Q0,Q-1)=(1,0) więc odejmujemy  A = A - M
000100|011011|0  |  ASR (5)
000010|001101|1  |  (Q0,Q-1)=(1,1) więc ASR (6)
000001|000110|1  |  KONIEC

powstała liczba to 000001000110 (w formacie xxxx.xxxxxxxx) = 0000.01000110

0000.01000110 = 1/4 + 1/64 + 1/128 = 32/128 + 2/128 + 1/128 = 35/128

 000010
+111011
-------
 111101

 111111
-111011
-------
 000100


format xx.xx
x = 1 1/4 = 1/4 * 2^2 = 01  cała liczba = 01.01
y = 3/4 = 3/4 * 2^2 = 11    cała liczba = 00.11

 A = 0 , Q = Y = 00.11, M = X = 01.01, Q - 1 = 00

 A  | Q  |Q-1|   Operacja
--------------------------
0000|0011|0  |  10 - > A = A - M
1011|0011|0  |  ASR (1)
1101|1001|1  |  11 - > ASR (2)
1110|1100|1  |  01 - > A = A + M
0011|1100|1  |  ASR (3)
0001|1110|0  |  00 - > ASR (4)
0000|1111|0  |  KONIEC


1110
0101
----
0011

powstała liczba to 00001111 ( w formacie xxxx.xxxx) = 0000.1111

0000.1111 = 1/2 + 1/4 + 1/8 + 1/16 = 15/16