1. Multiplication and Division Lab 9

2. Multiplication 13 x11 13 143 = 8Fh 1101 x1011 1101 100111 0000 100111 1101 10001111

3. Multiplication 1101 x1011 1101 100111 0000 100111 1101 10001111 1101 00001011 01101101 adsh 1101 10011110 adsh 1001111 sh 1101 10001111 adsh

4. Multiplication UM* ( u1 u2 -- upL upH ) TN N2 mpp (multiply partial product) if N(0) = 1 then adsh else sh end if; : UM* ( u1 u2 -- ud) LIT 0 mpp mpp ROT DROP ; All other signed and unsigned multiplication can be derived from UM*

5. y1 Modifications for Multiplication and Division

6. variable AVector: STD_LOGIC_VECTOR (width downto 0); variable BVector: STD_LOGIC_VECTOR (width downto 0); variable CVector: STD_LOGIC_VECTOR (width downto 0); variable yVector: STD_LOGIC_VECTOR (width downto 0); variable y1_tmp: STD_LOGIC_VECTOR (width-1 downto 0); AVector := '0' & a; BVector := '0' & b; CVector := '0' & c; y1_tmp := false; yVector := '0' & false; begin

7. when "011101" =>-- mpp if b(0) = '1' then yVector := AVector + CVector; else yVector := AVector; end if; y <= yVector(width downto 1); y1 <= yVector(0) & b(width-1 downto 1); mpp (multiply partial product) if N(0) = 1 then adsh else sh end if; TN N2

8. : UM* ( u1 u2 - upL upH ) 0 mpp mpp ROT_DROP ; 16 x 16 = 32 Multiplication

9. Division 1101 10000111 1010 1101 00111 0000 01111 1101 00101 0000 0101 13 135 13 05 10

10. Division 8-bit/4-bit = 4:4 1101 10000111 1010 1101 00111 0000 01111 1101 00101 0000 0101 _10000111 1101 numer[8:0] denom[3:0] If denom < numer[7:4] then overflow (quotient won’t fit in 4 bits) Let T = numer[8:4] N = numer[3:0] N2 = denom[3:0]

11. Division 8-bit/4-bit = 4:4 1101 10000111 1010 1101 00111 0000 01111 1101 00101 0000 0101 100001110 1101 sll TN N2 for I in 0 to 3 loop sll T & N; if T[8:4] > N2 then T := T - (0 & N2); N(0) := ‘1’; end if; end loop;

12. Division 8-bit/4-bit = 4:4 1101 10000111 1010 1101 00111 0000 01111 1101 00101 0000 0101 100001110 1101 sll TN N2 001111110 1101 sub1sll 011111100 1101 sll 001011010 sub1sll rem quot

13. Division : UM/MOD ( unumL unumH udenom -- urem uquot ) All other signed and unsigned division operations can be derived as WHYP words from UM/MOD TN N2 TN -ROT\ udenom unumL unumH SHLDC SHLDC \ denom quot rem ROT_DROP_SWAP ;

14. when "011110" =>-- shldc yVector := a & b(width-1); y1_tmp := b(width-2 downto 0) & '0'; if yVector > CVector then yVector := yVector - CVector; y1_tmp(0) := '1'; end if; for I in 0 to 3 loop sll T & N; if T[8:4] > N2 then T := T - (0 & N2); N(0) := ‘1’; end if; end loop; 100001110 1101 sll TN N2 y <= yVector(width-1 downto 0); y1 <= y1_tmp;

15. 32 / 16 = 16:16 Division : UM/MOD ( unL unH ud -- ur uq ) -ROT shldc shldc ROT_DROP_SWAP ;

16. Hex Division EE BC2F C C x E = A8 C x E = A8 + A = B2 B28 9AF A

17. Hex Division EE BC2F C A x E = 8C A x E = 8C + 8 = 94 B28 9AF A 94C 63 Dividend = BC2F Divisor = EE Quotient = CA Remainder = 63