Multi-Base Calculator CSE378 Final Project

1
Multi-Base CalculatorCSE378 Final Project

• By Matthew Lehn Yanqing Zhu
• December 17, 2001
• Professor Haskell

2
What About it?

• Its a calculator created from the original W8Y
  Microprocessor in Lab 9
• Supports unsigned operands and results
• Can accept operands in hexadecimal, decimal, or
  octal Returns the result in the same base
• Adds, subtracts, multiplies, divides

3
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 users
  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.

4
Lab 9 Mods contd - Schematic
M
5
Lab 9 Mods contd Seg7Dec.vhd
entity 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" gt AtoG lt
"0000001" -- zero . . .
when "0100" gt AtoG lt "1001100"
-- 4 when "0101" gt AtoG lt
"0100100" -- 5 or S when "0110" gt
if flag "11111" then
AtoG lt "0011000" -- P else
AtoG lt "0100000" -- 6
end if
when "0111" gt if flag
"11111" then AtoG lt "0011001"
-- r else AtoG lt
"0001101" -- 7 end if
when "1000" gt AtoG lt "0000000"
-- 8 . . . when others gt
AtoG lt "1111110" -- "dash" end
case end process end seg7dec_arch
6
Lab 9 Mods contd

• Due 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, jnbtn1, jnbtn2, jnbtn4
• Implemented the tof and ffetch commands
• tof -gt Send T(40) to the 5-bit statusReg
• ffetch -gt Fetch into T whatever is in the
  statusReg
• Added a drop_swap command (1 clk cycle)
• Drop T, T lt N2, N is unchanged

7
Lab 9 Mods w8y_control.vhd

• when drop_swap gt
• tsel lt "10" tload lt '1' dpop lt '1'
• when tof gt
• -- Pop T and push it onto the flag register
• tsel lt "11" tload lt '1' nsel lt "10"
  nload lt '1'
• dpop lt '1' fload lt '1'
• when ffetch gt
• -- Copy F from status register to T and push
  data stack
• tsel lt "01" tload lt '1' nload lt '1'
  dpush lt '1'
• dssel lt "11"
• when jz gt
• pload lt not z pinc lt z tsel lt "11" tload
  lt '1'
• nsel lt "10" nload lt '1' dpop lt '1'

8
Lab 9 Mods contd

• 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)

9
ALU4.VHD W8Y_CONTROL.VHD
when "1111" gt -- N T (will display a carry)
yVector AVector BVector -- 9 bits, 1
for the carry y2_tmp(0) yVector(width)
y2 lt yVector(width-1 downto 0) -- Store sum
(minus carry) into N y lt y2_tmp
-- Store carry bit into T
when plus_carry gt -- 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 lt '1' nsel lt "00" nload lt
'1' alusel lt "1111" when mpp gt tload lt
'1' nsel lt "00" nload lt '1' alusel lt
"1101" when shldc gt tload lt '1' nsel lt
"00" nload lt '1' alusel lt "1110"
Note The rest of ALU4.VHD resembles the lecture
notes for MPP and SHLDC.
10
Convert_in Function

• Basic Idea
• If entering 49 into the calculator
• The input BCD number isnt real 49 its only 2
  digits 4 9 !
• Represented as 0100 1001
• The real 49 4 10 9

11
Convert_in Function
S N2 N T
49
49 49

49 4
49 4 A
49 28 00
28 49

28 90

28 9
31

• CONVERT_IN ( BCD/BCO -- BIN )
• DUP
• 4 FOR
• U2/
• NEXT \ get higher 4
  bits
• F_at_ \ fetch the
  base
• UM \ TN 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

12
Convert_out Function

• Basic Idea
• The convert_out function is just the reverse of
  the convert_in function, i.e.
• 4 9 4A9 (31)16
• INPUT
  CONVERT_IN
• 4 9 (31)16 /A 49
• OUTPUT
  CONVERT_OUT

13
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)

14
Convert_out_8 Function
CONVERT_OUT_8 ( Bin -- BCD/BCO )
0 \ Push higher 8 bits of result into
T F_at_ \ Get base from statusReg
UM/MOD \ Convert
4 FOR \ Shift
combine the answer 2
NEXT \ HBit LBit SWAP
15
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)

16
Convert_out_16 Function
CONVERT_OUT_16 ( BinL BinL -- BCDL/BCOL
BCDH/BCOH ) 3 FOR
F_at_ 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
17
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 ) gtR 0 R_at_
\ udL udH 0 un UM/MOD \
udl remH quotH Rgt \ udL
remH quotH un SWAP gtR \ udL
remH un
UM/MOD \ remL quotL Rgt
\ remL quotL quotH CONVERT_IN ( fakebin --
realbin ) \ Convert BCD to real binary DUP
4 FOR \
Get the higher bits (shift right) U2/
NEXT F_at_ \ 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_at_ MU/MOD \ Divide by base-
return dbl quot NEXT DROP \ Drop
00 in T
18
WHYP it Up Contd
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_at_ \ 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_at_
DELAY CONVERT_IN \ to specified base waitbtn3
SW_at_ DELAY CONVERT_IN waitbtn3
main ( -- ) BEGIN 5E \ Display BASE BA
waitbtn3 DROP DROP \ Get rid of BA5E in T N
regs TRUE gtF \ Set flag to TRUE so
OPER is displayed SW_at_ \ 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 gtF \ Turn
off P R display mode SW_at_ \ 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 gtF \ Save base in statusReg
put oper in T DUP \ Duplicate oper into
N C0 \ Division IF
19
WHYP it Up Contd
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
20
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, --0
• X"83", --1
• LIT, -- DELAY
• X"f5", --3
• tor, --4
• drjne, --5
• X"05", --6
• RET, --7
• minus, --
• zeroequal, --9
• RET, --a
• LIT, -- UM
• X"00", --c
• LIT, --d
• X"08", --e
• tor, --f

X"04", --37 tor, --38 twotimes, --39 drjne,
--3a X"39", --3b LIT, --3c X"04",
--3d tor, --3e u2slash, --3f drjne,
--40 X"3f", --41 plus, --42 RET,
--43 LIT, -- conv_out_16 X"03", --45 tor,
--46 ffetch, --47 CALL, --48 X"1e",
--49 drjne, --4a X"47", --4b drop,
--4c LIT, --4d X"04", --4e tor,
--4f twotimes, --50 drjne, --51 X"50",
--52 plus, --53
drjne, --1a X"19", --1b ROT_DROP_SWAP,
--1c RET, --1d tor, -- MU/MOD LIT,
--1f X"00", --20 rfetch, --21 CALL,
--22 X"15", --23 rfrom, --24 swap,
--25 tor, --26 CALL, --27 X"15",
--28 rfrom, --29 RET, --2a dup, --
convert_in LIT, --2c X"04", --2d tor,
--2e u2slash, --2f drjne, --30 X"2f",
--31 ffetch, --32 CALL, --33 X"0b",
--34 drop_swap, --35 LIT, --36
21
Compiled w8y_rom (2/3)

• mrot, --54
• LIT, --55
• X"04", --56
• tor, --57
• twotimes, --58
• drjne, --59
• X"58", --5a
• plus, --5b
• swap, --5c
• RET, --5d
• LIT, --5e
• X"00", -- conv_out_8
• ffetch, --60
• CALL, --61
• X"15", --62
• LIT, --63
• X"04", --64
• tor, --65
• twotimes, --66

CALL, --71 X"02", --72 CALL, --73 X"2b",
--74 JBTN3, --75 X"75", --76 JNBTN3,
--77 X"77", --78 swfetch, --79 CALL,
--7a X"02", --7b CALL, --7c X"2b",
--7d JBTN3, --7e X"7e", --7f JNBTN3,
--80 X"80", --81 RET, --82 LIT, --
MAIN X"5e", --84 LIT, --85 X"ba",
--86 JBTN3, --87 X"87", --88 JNBTN3,
--89 X"89", --8a drop, --8b drop,
--8c ones, --8d tof, --8e swfetch,
--8f dup, --90
LIT, --91 X"e7", --92 LIT, --93 X"06",
--94 JBTN3, --95 X"95", --96 JNBTN3,
--97 X"97", --98 drop, --99 zeros,
--9a tof, --9b swfetch, --9c tuck,
--9d plus, --9e ldstore, --9f swap,
--a0 tof, --a1 dup, --a2 LIT, --a3 X"c0",
-- DIVIDE CALL, --a5 X"08", --a6 JZ,
--a7 X"b7", --a8 drop, --a9 CALL,
--aa X"6c", --ab LIT, --ac X"00", --ad
22
Compiled w8y_rom (3/3)

• swap, --ae
• CALL, --af
• X"15", --b0
• CALL, --b1
• X"5e", --b2
• CALL, --b3
• X"5e", --b4
• JMP, --b5
• X"d9", --b6
• dup, --b7
• LIT, --b8
• X"80", -- MULTIPLY
• CALL, --ba
• X"08", --bb
• JZ, --bc
• X"c7", --bd
• drop, --be
• CALL, --bf
• X"6c", --c0

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 )
23
(No Transcript)
24
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 cant perform (1 - F) or (-2
  5).

25
Any questions?