1. Design of Networks for Arithmetic Operation
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2. Table 4-1 Operation of Serial Adder
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3. Fig. 4-2 Control State Graph and Table for Serial Adder
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4. State Graph for Control Networks
Constraints on Input Labels for Every State Sk
1. If Ii and Ij are any pair of input labels on arcs exiting state Sk, then IiIj = 0 if i ¹ j.
2. If n arcs exit state Sk and the n arcs have input labels I1, I2, ..., In, respectively, then I1 + I In = 1.
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5. Example 1
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6. Example - 2
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7. Design of a Binary Mulitplier
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17. Multiplication of Signed Binary Numbers
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24. Figure 4-12(a) Behavioural Model for 2’s Complement Multiplier
library BITLIB;
use BITLIB.bit_pack.all;
entity mult2C is
port (CLK, St: in bit;
Mplier,Mcand : in bit_vector(3 downto 0);
Product: out bit_vector (6 downto 0);
Done: out bit);
end mult2C;
architecture behave1 of mult2C is
signal State : integer range 0 to 5;
signal A, B: bit_vector(3 downto 0);
alias M: bit is B(0);
begin
process
variable addout: bit_vector(4 downto 0);
wait until CLK = '1';
case State is
when 0=> -- initial State
if St='1' then
A <= "0000"; -- Begin cycle
B <= Mplier; -- load the multiplier
State <= 1;
end if;
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25. Figure 4-12(b) Behavioral Model for 2’s Complement Multiplier
when 1 | 2 | 3 => -- "add/shift" State
if M = '1' then
addout := add4(A,Mcand,'0'); -- Add multiplicand to A and shift
A <= Mcand(3) & addout(3 downto 1);
B <= addout(0) & B(3 downto 1);
else
A <= A(3) & A(3 downto 1); -- Arithmetic right shift
B <= A(0) & B(3 downto 1);
end if;
State <= State + 1;
when 4 => -- add complement if sign bit
if M = '1' then -- of multiplier is 1
addout := add4(A, not Mcand,'1');
A <= not Mcand(3) & addout(3 downto 1);
State <= 5; wait for 0 ns;
Done <= '1'; Product <= A(2 downto 0) & B;
when 5 => -- output product
State <= 0;
Done <= '0';
end case;
end process;
end behave1;
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26. Figure 4-13 Command File and Simulation Results for (+5/8 by -3/8)
-- command file to test signed multiplier
list CLK St State A B Done Product
force st 1 2, 0 22
force clk 1 0, repeat 20
-- (5/8 * -3/8)
force Mcand 0101
force Mplier 1101
run 120
ns delta CLK St State A B Done Product
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27. Figure 4-14 Test Bench for Signed Multiplier
library BITLIB;
use BITLIB.bit_pack.all;
entity testmult is end testmult;
architecture test1 of testmult is
component mult2C
port(CLK, St: in bit;
Mplier,Mcand : in bit_vector(3 downto 0);
Product: out bit_vector (6 downto 0);
Done: out bit);
end component;
constant N: integer := 11; type arr is array(1 to N) of bit_vector(3 downto 0);
constant Mcandarr: arr := ("0111", "1101", "0101", "1101", "0111", "1000", "0111",
"1000", "0000", "1111", "1011");
constant Mplierarr: arr := ("0101", "0101", "1101", "1101", "0111", "0111", "1000",
"1000", "1101", "1111", "0000");
signal CLK, St, Done: bit; signal Mplier, Mcand: bit_vector(3 downto 0);
signal Product: bit_vector(6 downto 0);
begin
CLK <= not CLK after 10 ns;
process
for i in 1 to N loop
Mcand <= Mcandarr(i); Mplier <= Mplierarr(i); St <= '1';
wait until rising_edge(CLK); St <= '0'; wait until falling_edge(Done);
end loop;
end process;
mult1: mult2c port map(Clk, St, Mplier, Mcand, Product, Done);
end test1;
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28. Parallel Divider for Positive Binary Numbers
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30. Figure 4-19 Block Diagram for Parallel Binary Divider
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31. Figure 4-20 State Diagram for Divider Control Circuit
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33. Control Signals for Signed Divider
LdU Load upper half of dividend from bus
LdL Load lower half of dividend from bus
Lds Load sign of dividend into sign flip-flop
S Sign of dividend
Cm1 Complement dividend register (2's complement)
Ldd Load divisor from bus
Su Enable adder output onto bus (Ena) and load upper half of dividend from bus
Cm2 Enable complementer (Cm2 equals the complement of the sign bit of the divisor,
so that a positive divisor is complemented and a negative divisor is not)
Sh Shift the dividend register left one place and increment the counter
C Carry output from adder (If C = 1, the divisor can be subtracted from the upper
dividend.)
St Start
V Overflow
Qneg Quotient will be negative (Qneg = 1 when sign of dividend and divisor are
different)
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34. Figure 4-21 Block Diagram for Signed Divider
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35. Figure 4-22 State Graph for Signed Divider Control Network
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36. Figure 4-23(a) VHDL Model of 32-bit Signed Divider
library BITLIB;
use BITLIB.bit_pack.all;
entity sdiv is
port(Clk,St: in bit;
Dbus: in bit_vector(15 downto 0); Quotient: out bit_vector(15 downto 0);
V, Rdy: out bit);
end sdiv;
architecture Signdiv of Sdiv is
constant zero_vector: bit_vector(31 downto 0):=(others=>'0');
signal State: integer range 0 to 6; signal Count : integer range 0 to 15;
signal Sign,C,NC: bit; signal Divisor,Sum,Compout: bit_vector(15 downto 0);
signal Dividend: bit_vector(31 downto 0);
alias Q: bit_vector(15 downto 0) is Dividend(15 downto 0);
alias Acc: bit_vector(15 downto 0) is Dividend(31 downto 16);
begin -- concurrent statements
compout <= divisor when divisor(15) = '1' -- 1's complementer
else not divisor;
Addvec(Acc,compout,not divisor(15),Sum,C,16); bit adder
Quotient <= Q; Rdy <= '1' when State=0 else '0';
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37. Figure 4-23(b) VHDL Model of 32-bit Signed Divider
process
begin
wait until Clk = '1'; -- wait for rising edge of clock
case State is
when 0=>
if St = '1' then
Acc <= Dbus; -- load upper dividend
Sign <= Dbus(15); State <= 1;
V <= '0'; Count <= 0; -- initialize overflow// initialize counter
end if;
when 1=>
Q <= Dbus; State <= 2; -- load lower dividend
when 2=>
Divisor <= Dbus;
if Sign ='1'then -- two's complement Dividend if necessary
addvec(not Dividend,zero_vector,'1',Dividend,NC,32);
end if; State <= 3;
when 3=>
Dividend <= Dividend(30 downto 0) & '0'; -- left shift
Count <= Count+1; State <= 4;
when 4 =>
if C ='1' then -- C
v <= '1'; State <= 0;
else -- C'
Count <= Count+1; State <= 5;
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38. Figure 4-23(c) VHDL Model of 32-bit Signed Divider
when 5 =>
if C = '1' then -- C
ACC <= Sum; -- subtract
Q(0)<= '1';
else
Dividend <= Dividend(30 downto 0) & '0'; -- left shift
if Count = 15 then -- KC'
count<= 0; State <= 6;
else Count <= Count+1;
end if;
when 6=>
Acc <= Sum; -- subtract
Q(0) <= '1';
else if (Sign xor Divisor(15))='1' then -- C'Qneg
addvec(not Dividend,zero_vector,'1',Dividend,NC,32);
end if; -- 2's complement Dividend
state <= 0;
end case;
end process;
end signdiv;
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