multi-base calculator cse378 final project

Multi-Base CalculatorMulti-Base CalculatorCSE378 Final ProjectCSE378 Final Project

By Matthew Lehn & Yanqing ZhuDecember 17, 2001

Professor Haskell

What About it?

It’s a calculator created from the original W8Y Microprocessor in Lab 9Supports unsigned operands and resultsCan accept operands in hexadecimal, decimal, or octal – Returns the result in the same baseAdds, subtracts, multiplies, & divides

Lab 9 Modifications

Our 7-segment display needs to show BASE and OPER, however, only the characters 0-F existed in seg7dec.vhd. We created a 1-bit register to store a “flag”. When the

flag is TRUE, P and R replace the characters 6 and 7.

We also need some place to store the user’s specified BASE. Since the data stack and return stack are inconvenient

spots and would require additional operations to retrieve, we decided to make the flag/status register to 5-bits.

ReturnStack

RmuxPmux

PCclrclk

pload

pinc

IRclrclkirload

W8Y_rom

W8Y_control

plus1

R

DS

Rin

R T

P

Pin

M

M P1

R

M

SW(1:8)

LDreg

LD(1:8)

T

ldloadclkclr

step_display

A(3:0) AtoG(6:0)

clk

clr

TN

BTN(1)

BTN(4)

clr

step

The W8YMicrocontroller

clkclr

rpop

rpush

psel rinsel

dssel(1:0)

rload

rdec

rsel

T

icode

E

BTN(1:4)

DataStack_ALUclkclr

dpop

dpush

ssel

nloadnsel

tload

tsel(1:0)

alusel(3:0)

T

0 11

1

0

0 2 3DSmux

T(4:0)

fload

M

StatusREG

●

F

clr

clk

●

●

clr clk

Lab 9 Mods cont’d - Schematic

M

Lab 9 Mods cont’d – Seg7Dec.vhdentity seg7dec is

port (q: in STD_LOGIC_VECTOR(3 downto 0);

flag: in STD_LOGIC_VECTOR(4 downto 0);

AtoG: out STD_LOGIC_VECTOR(6 downto 0));

end seg7dec;

architecture seg7dec_arch of seg7dec is

begin

process(q, flag)

begin

case q is

when "0000" =>

AtoG <= "0000001"; -- zero

. . .

when "0100" =>

AtoG <= "1001100"; -- 4

when "0101" =>

AtoG <= "0100100"; -- 5 or S

when "0110" =>

if flag = "11111" then

AtoG <= "0011000"; -- P

else

AtoG <= "0100000"; -- 6

end if;

when "0111" =>

if flag = "11111" then

AtoG <= "0011001"; -- r

else

AtoG <= "0001101"; -- 7

end if;

when "1000" =>

AtoG <= "0000000"; -- 8

. . .

when others =>

AtoG <= "1111110"; -- "dash"

end case;

end process;

end seg7dec_arch;

Lab 9 Mods – cont’dDue to space constraints, we removed several opcodes from w8y_codes.vhd and w8y_control.vhd. nop, over, nip, plus1, minus1, andd, orr, xorr,

twoslash, rfromdrop, j[n]btn1, j[n]btn2, j[n]btn4

Implemented the tof and ffetch commands tof -> Send T(4:0) to the 5-bit statusReg ffetch -> Fetch into T whatever is in the statusReg

Added a drop_swap command (1 clk cycle) Drop T, T <= N2, N is unchanged

Lab 9 Mods – w8y_control.vhdwhen drop_swap =>

tsel <= "10"; tload <= '1'; dpop <= '1';

when tof =>

-- Pop T and push it onto the flag register

tsel <= "11"; tload <= '1'; nsel <= "10"; nload <= '1';

dpop <= '1'; fload <= '1';

when ffetch =>

-- Copy F from status register to T and push data stack

tsel <= "01"; tload <= '1'; nload <= '1'; dpush <= '1';

dssel <= "11";

when jz =>

pload <= not z; pinc <= z; tsel <= "11"; tload <= '1';

nsel <= "10"; nload <= '1'; dpop <= '1';

Lab 9 Mods – cont’d

We expanded ALU4.vhd to include:Multiplication (mpp)

Nmux in the DS_ALU component changed to allow 4 inputs. A signal y2 was added into the MUX.

ALU can now accept T, N, AND N2 as inputs.Division (shldc)Addition w/ Carry (+C)

ALU4.VHD & W8Y_CONTROL.VHD

Note: The rest of ALU4.VHD resembles the lecture notes for MPP and SHLDC.

when "1111" => -- N + T (will display a carry)

yVector := AVector + BVector; -- 9 bits, 1 for the carry

y2_tmp(0) := yVector(width);

y2 <= yVector(width-1 downto 0); -- Store sum (minus carry) into N

y <= y2_tmp; -- Store carry bit into T

when plus_carry =>

-- Use when actually wanting to add two numbers as an

-- operation and NOT for intermediate steps requiring

-- addition. This function displays the carry, if it exists

tload <= '1'; nsel <= "00"; nload <= '1'; alusel <= "1111";

when mpp =>

tload <= '1'; nsel <= "00"; nload <= '1'; alusel <= "1101";

when shldc =>

tload <= '1'; nsel <= "00"; nload <= '1'; alusel <= "1110";

Convert_in Function

• Basic Idea

If entering “49” into the calculator: The input BCD number isn’t real 49 it’s only 2 digits 4 & 9 ! Represented as 0100 1001 The real 49 = 4 * 10 + 9

Convert_in Function

: CONVERT_IN ( BCD/BCO -- BIN )

DUP

4 FOR

U2/

NEXT \ get higher 4 bits

F@ \ fetch the base

UM* \ T*N return 16 bits

DROP_SWAP \ drop + swap

4 FOR

2*

NEXT \ shift out the lower 4 bits

4 FOR

U2/

NEXT \ get the higher 4 bits

+ ; \ Hbits+ Lbits

S N2 N T

49

49 49

49 4

49 4 A

49 28 00

28 49

28 90

28 9

31

Convert_out Function

• Basic Idea

The convert_out function is just the reverse of the convert_in function, i.e.

4 & 9 4*A+9 = (31)16 INPUT CONVERT_IN

4 & 9 (31)16 /A = 4…9 OUTPUT CONVERT_OUT

Convert_out_8 Function• Convert_out_8

Convert 8 bit number, used only for Subtraction & Division

Operation Quotient/Difference Remainder

Subtraction 0 ~ 99(Dec)

0 ~ 77(Oct)

0 ~ FF(Hex)

Division 0 ~ 99(Dec) 0 ~ 49 (Dec: 99/50)

0 ~ 77(Oct) 0 ~ 37 (Oct: 77/40)

0 ~ FF(Hex) 0 ~ 7F (Hex: FF/80)

Convert_out_8 Function

: CONVERT_OUT_8 ( Bin -- BCD/BCO )

0 \ Push higher 8 bits of result into T

F@ \ Get base from statusReg

UM/MOD \ Convert

4 FOR \ Shift & combine the answer

2*

NEXT

+ \ HBit + LBit

SWAP ;

Convert_out_16 Function

• Convert_out_16

Convert 16 bit number, used only for Addition & Multiplication

Operation Product/Sum

Addition 0 ~ 198(Dec)

0 ~ 176(Oct)

0 ~ 1FE(Hex)

Multiplication 0 ~ 9801(Dec)

0 ~ 7601(Oct)

0 ~ FE01(Hex)

Convert_out_16 Function : CONVERT_OUT_16 ( BinL BinL -- BCDL/BCOL BCDH/BCOH )

3 FOR

F@ MU/MOD \ Divide by base & return dbl quotient

NEXT

DROP \ Drop 00 in T

4 FOR \ T= bit 15-12 of the answer

2* \ Shift it to higher bits

NEXT

+ \ N= bit11-8 + bit15-12= bit15-8

-ROT \ N= bit7-4, put it in T

4 FOR

2* \ Shift bit7-4 to the higher positions

NEXT

+ \ N= bit3-0 + bit7-4= bit7-0 (in T)

SWAP ; \ Swap bit15-8 w/ bit7-0

WHYP it Up!HEX

: DELAY ( -- )

F5 FOR NEXT ;

: = ( n1 n2 -- f )

- 0= ;

: UM* ( u1 u2 -- ud )

0

8 FOR

mpp

NEXT

ROT_DROP ;

: UM/MOD ( unumL unumH udenom -- urem uquot )

-ROT

8 FOR

shldc

NEXT

ROT_DROP_SWAP ;

: MU/MOD ( ud un -- urem udquot )

>R 0 R@ \ udL udH 0 un

UM/MOD \ udl remH quotH

R> \ udL remH quotH un

SWAP >R \ udL remH un

UM/MOD \ remL quotL

R> ; \ remL quotL quotH

: CONVERT_IN ( fakebin -- realbin ) \ Convert BCD to real binary

DUP

4 FOR \ Get the higher bits (shift right)

U2/

NEXT

F@ \ Get the base from statusReg

UM* \ Convert the higher bits

DROP_SWAP \ Drop the 00 & load lower bits

4 FOR \ Get rid of the higher bits

2*

NEXT

4 FOR \ Shift back the lower bits

U2/

NEXT

+ ; \ HBit + LBit = real binary

: CONVERT_OUT_16 ( bin -- fakebin ) \ Convert binary to designated base -- Used for addition & multiplication

3 FOR

F@ MU/MOD \ Divide by base- return dbl quot

NEXT

DROP \ Drop 00 in T

WHYP it Up – Cont’d 4 FOR \ T= bit 15-12 of the answer

2* \ Shift it to higher bits

NEXT

+ \ N= bit11-8 + bit15-12= bit15-8

-ROT \ N= bit7-4, put it in T

4 FOR

2* \ Shift bit7-4 to the higher positions

NEXT

+ \ N= bit3-0 + bit7-4= bit7-0 (in T)

SWAP ; \ Swap bit15-8 w/ bit7-0

: CONVERT_OUT_8 \ Convert binary to designated base

\ Used for subtraction & division

0 \ Push higher 8 bits of result into T

F@ \ Get base from statusReg

UM/MOD \ Convert

4 FOR \ Shift & combine the answer as above

2*

NEXT

+ \ HBit + LBit

SWAP ;

: GET2_N_CONVERT ( -- u1 u2 ) \ Fetch & convertt

waitbtn3 SW@ DELAY CONVERT_IN \ to specified base

waitbtn3 SW@ DELAY CONVERT_IN

waitbtn3 ;

: main ( -- )

BEGIN

5E \ Display BASE

BA

waitbtn3

DROP DROP \ Get rid of BA5E in T & N regs

TRUE

>F \ Set flag to TRUE so OPER is displayed

SW@ \ Fetch the base (switches 4-8)

DUP \ Copy base to N for later use

E7 \ Display OPER

06

waitbtn3

DROP \ Drop 06 from T, put E7 in T

FALSE \ Overwrite E7 in T with zeros

>F \ Turn off P & R display mode

SW@ \ Fetch operation (switches 1-2)

TUCK + \ Place oper in N2 and add N & T

LD! \ Light LEDs to signify base and oper

SWAP \ Put base in T and oper in N

>F \ Save base in statusReg; put oper in T

DUP \ Duplicate oper into N

C0 = \ Division

IF

WHYP it Up – Cont’d

DROP \ Remove oper

GET2_N_CONVERT \ Get 2 operands & convert to base

0 SWAP \ Set high bits to 0 (8/8 div only)

UM/MOD \ Divide N2 by T (N is 0)

CONVERT_OUT_8 \ Convert quotient to base

CONVERT_OUT_8 \ Convert remainder to base

ELSE

DUP

80 = \ Multiplication

IF

DROP \ Remove OPER

GET2_N_CONVERT

UM* \ Multiply T & N

CONVERT_OUT_16

ELSE

40 = \ Subtraction

IF

GET2_N_CONVERT

- \ Subtract T from N

CONVERT_OUT_8

ELSE \ Addition

GET2_N_CONVERT

+C \ Add T & N; store carry in T

CONVERT_OUT_16

THEN

THEN

THEN

waitbtn3 \ Hold answer on display

AGAIN ;

Compiled w8y_rom (1/3)type rom_array is array (0 to 223) of STD_LOGIC_VECTOR (7 downto 0);constant rom: rom_array := (

JMP, --0X"83", --1LIT, -- :DELAYX"f5", --3tor, --4drjne, --5X"05", --6RET, --7minus, -- :=zeroequal, --9RET, --aLIT, -- :UM*X"00", --cLIT, --dX"08", --etor, --fmpp, --10drjne, --11X"10", --12ROT_DROP, --13RET, --14mrot, -- :UM/MODLIT, --16X"08", --17tor, --18shldc, --19

drjne, --1aX"19", --1bROT_DROP_SWAP, --1cRET, --1dtor, -- :MU/MODLIT, --1fX"00", --20rfetch, --21CALL, --22X"15", --23rfrom, --24swap, --25tor, --26CALL, --27X"15", --28rfrom, --29RET, --2adup, -- :convert_inLIT, --2cX"04", --2dtor, --2eu2slash, --2fdrjne, --30X"2f", --31ffetch, --32CALL, --33X"0b", --34drop_swap, --35LIT, --36

X"04", --37tor, --38twotimes, --39drjne, --3aX"39", --3bLIT, --3cX"04", --3dtor, --3eu2slash, --3fdrjne, --40X"3f", --41plus, --42RET, --43LIT, -- :conv_out_16X"03", --45tor, --46ffetch, --47CALL, --48X"1e", --49drjne, --4aX"47", --4bdrop, --4cLIT, --4dX"04", --4etor, --4ftwotimes, --50drjne, --51X"50", --52plus, --53

Compiled w8y_rom (2/3)mrot, --54LIT, --55X"04", --56tor, --57twotimes, --58drjne, --59X"58", --5aplus, --5bswap, --5cRET, --5dLIT, --5eX"00", -- :conv_out_8ffetch, --60CALL, --61X"15", --62LIT, --63X"04", --64tor, --65twotimes, --66drjne, --67X"66", --68plus, --69swap, --6aRET, --6bJBTN3, -- :get2_n_convX"6c", --6dJNBTN3, --6eX"6e", --6fswfetch, --70

CALL, --71X"02", --72CALL, --73X"2b", --74JBTN3, --75X"75", --76JNBTN3, --77X"77", --78swfetch, --79CALL, --7aX"02", --7bCALL, --7cX"2b", --7dJBTN3, --7eX"7e", --7fJNBTN3, --80X"80", --81RET, --82LIT, -- :MAINX"5e", --84LIT, --85X"ba", --86JBTN3, --87X"87", --88JNBTN3, --89X"89", --8adrop, --8bdrop, --8cones, --8dtof, --8eswfetch, --8fdup, --90

LIT, --91X"e7", --92LIT, --93X"06", --94JBTN3, --95X"95", --96JNBTN3, --97X"97", --98drop, --99zeros, --9atof, --9bswfetch, --9ctuck, --9dplus, --9eldstore, --9fswap, --a0tof, --a1dup, --a2LIT, --a3X"c0", -- DIVIDECALL, --a5X"08", --a6JZ, --a7X"b7", --a8drop, --a9CALL, --aaX"6c", --abLIT, --acX"00", --ad

Compiled w8y_rom (3/3)swap, --aeCALL, --afX"15", --b0CALL, --b1X"5e", --b2CALL, --b3X"5e", --b4JMP, --b5X"d9", --b6dup, --b7LIT, --b8X"80", -- MULTIPLYCALL, --baX"08", --bbJZ, --bcX"c7", --bddrop, --beCALL, --bfX"6c", --c0CALL, --c1X"0b", --c2CALL, --c3X"44", --c4JMP, --c5X"d9", --c6LIT, --c7X"40", --

SUBTRACTCALL, --c9X"08", --ca

JZ, --cb X"d4", --cc CALL, --cd X"6c", --ce minus, --cf CALL, --d0 X"5e", --d1 JMP, --d2 X"d9", --d3 CALL, -- ADD X"6c", --d5 plus_carry, --d6 CALL, --d7 X"44", --d8 JBTN3, --d9 X"d9", --da JNBTN3, --db X"db", --dc JMP, --dd X"83", --de X"00" --df);

INSTRUCTIONS FOR THE W8Y MULTI-BASE CALCULATOR

STEP 1: Enter the BASE using the SW 4-8 and press BTN3

BASE Switch Possibilities SW 1 2 3 4 5 6 7 8 - - - 1 0 0 0 0 Hexadecimal (Base-16) - - - 0 1 0 1 0 Decimal (Base-10) - - - 0 1 0 0 0 Octal (Base-8) STEP 2: Using SW 1-2, select the OPERation you want performed and push BTN3

OPERation Switch Possibilities SW 1 2 3 4 5 6 7 8 0 0 - - - - - - Addition 0 1 - - - - - - Subtraction 1 0 - - - - - - Multiplication 1 1 - - - - - - Division

STEP 3: If the operation requested is ADDITION -- Set switches, push btn3, set switches, push btn3 SUBTRACTION -- Set switches, push btn3, set switches, push btn3 The second number entered is subtracted from the first MULTIPLICATION -- Set switches, push btn3, set switches, push btn3 DIVISION -- Set switches, push btn3, set switches, push btn3 You can only divide 8 bits by 8 bits. The numerator is first. Notes:

After each BTN3 push, the number will be displayed in its original form for a few seconds. For decimal and octal, enter your numbers as BCD (binary coded decimal)

Example: For 15 in Decimal, SW1-8 should be 00010101 For 93 in Decimal, SW1-8 should be 10010011

For 17 in Octal, SW1-8 should be 00010111 For 77 in Octal, SW1-8 should be 01110111

The maximum value for decimal is 99. For octal, the maximum is 77. STEP 4: After you input the two operands, press BTN3 again to display the result. The displayed result will be in your designated base. STEP 5: Press BTN1 to start over.

Conclusion

Unfortunately, since each simulation waveform is extraordinarily long and would take 10+ slides to cover, they will not be shown here. The result is not shown until 12,400 ns!

Note that the calculator will only accept positive operands and only display positive results. For instance, it can’t perform (1 - F) or (-2 * 5).