Magnitude Comparator Lecture L6.4 Section 6.1

4-Bit Equality Detector A_EQ_B B[3..0]

Magnitude Comparator A_LT_B A[3..0] Magnitude Detector A_EQ_B B[3..0] A_GT_B

Magnitude Comparator How can we find A_GT_B? How many rows would a truth table have? 28 = 256!

Magnitude Comparator Find A_GT_B Because A3 > B3 i.e. A3 & !B3 = 1 If A = 1001 and B = 0111 is A > B? Why? Therefore, one term in the logic equation for A_GT_B is A3 & !B3

Magnitude Comparator A_GT_B = A3 & !B3 # ….. Because A3 = B3 and # ….. Because A3 = B3 and A2 > B2 i.e. C3 = 1 and A2 & !B2 = 1 If A = 1101 and B = 1011 is A > B? Why? Therefore, the next term in the logic equation for A_GT_B is C3 & A2 & !B2

Magnitude Comparator A_GT_B = A3 & !B3 # C3 & A2 & !B2 # ….. # ….. Because A3 = B3 and A2 = B2 and A1 > B1 i.e. C3 = 1 and C2 = 1 and A1 & !B1 = 1 If A = 1010 and B = 1001 is A > B? Why? Therefore, the next term in the logic equation for A_GT_B is C3 & C2 & A1 & !B1

Magnitude Comparator A_GT_B = A3 & !B3 # C3 & A2 & !B2 # C3 & C2 & A1 & !B1 # ….. Because A3 = B3 and A2 = B2 and A1 = B1 and A0 > B0 i.e. C3 = 1 and C2 = 1 and C1 = 1 and A0 & !B0 = 1 If A = 1011 and B = 1010 is A > B? Why? Therefore, the last term in the logic equation for A_GT_B is C3 & C2 & C1 & A0 & !B0

Magnitude Comparator A_GT_B = A3 & !B3 # C3 & A2 & !B2 # C3 & C2 & A1 & !B1 # C3 & C2 & C1 & A0 & !B0

Magnitude Comparator Find A_LT_B A_LT_B = !A3 & B3 # C3 & !A2 & B2 # C3 & C2 & !A1 & B1 # C3 & C2 & C1 & !A0 & B0

ABEL Program MODULE magcomp4 TITLE '4-BIT COMPARATOR, R. Haskell, 9/21/02‘ DECLARATIONS " INPUT PINS " A3..A0 PIN 11, 7, 6, 5; A = [A3..A0]; B3..B0 PIN 4, 3, 2, 1; B = [B3..B0]; " OUTPUT PINS " A_EQ_B PIN 36; A_LT_B PIN 35; A_GT_B PIN 37; C3..C0 NODE; C = [C3..C0];

ABEL Program (cont.) EQUATIONS C = !(A $ B); A_EQ_B = C0 & C1 & C2 & C3; A_GT_B = A3 & !B3 # C3 & A2 & !B2 # C3 & C2 & A1 & !B1 # C3 & C2 & C1 & A0 & !B0; A_LT_B = !A3 & B3 # C3 & !A2 & B2 # C3 & C2 & !A1 & B1 # C3 & C2 & C1 & !A0 & B0;

ABEL Program (cont.) test_vectors ([A, B] -> [A_EQ_B, A_LT_B, A_GT_B]) [0, 0] -> [1, 0, 0]; [2, 5] -> [0, 1, 0]; [10, 12] -> [0, 1, 0]; [7, 8] -> [0, 1, 0]; [4, 2] -> [0, 0, 1]; [6, 6] -> [1, 0, 0]; [1, 7] -> [0, 1, 0]; [5, 13] -> [0, 1, 0]; [12, 0] -> [0, 0, 1]; [6, 3] -> [0, 0, 1]; [9, 9] -> [1, 0, 0]; [12, 13] -> [0, 1, 0]; [7, 0] -> [0, 0, 1]; [4, 1] -> [0, 0, 1]; [3, 2] -> [0, 0, 1]; [15, 15] -> [1, 0, 0]; END

TTL Comparators 1 2 3 4 5 6 7 9 10 11 12 8 19 20 17 18 15 16 13 14 GND Vcc P>Q P0 Q0 P1 Q1 P2 Q2 P3 Q3 P=Q Q7 P7 Q6 P6 Q5 P5 Q4 P4 74LS682 B3 A<Bin A=Bin A>Bin A>Bout A=Bout A<Bout A3 B2 A2 A1 B1 A0 B0 74LS85

Cascading two 74LS85s

Question Draw a logic circuit for what is in the green box. P_GT_Q P_EQ_Q P_LT_Q 1 2 3 4 5 6 7 9 10 11 12 8 19 20 17 18 15 16 13 14 GND Vcc P>Q P0 Q0 P1 Q1 P2 Q2 P3 Q3 P=Q Q7 P7 Q6 P6 Q5 P5 Q4 P4 74LS682 Draw a logic circuit for what is in the green box.

Answer Outputs: Y = !(P_GT_Q) Z = !(P_EQ_Q) P_GT_Q = !Y NOT GATE P_EQ_Q = !Z NOT GATE P_LT_Q = !(P_GT_Q) & !(P_EQ_Q) = Y & Z AND GATE P_LT_Q = !(P_GT_Q # P_EQ_Q) = !(!Y # !Z) NOR GATE

Comparator Using Behavioral ABEL MODULE comp4bit TITLE '4-BIT COMPARATOR, R. Haskell, 7/29/02' DECLARATIONS " INPUT PINS " A3..A0 PIN 11,7, 6, 5; A = [A3..A0]; B3..B0 PIN 4, 3, 2, 1; B = [B3..B0]; A_EQ_B PIN 36; A_LT_B PIN 35; A_GT_B PIN 37;

Comparator Using Behavioral ABEL EQUATIONS A_EQ_B = (A == B); A_GT_B = (A > B); A_LT_B = !((A == B) # (A > B));

Comparator Using Behavioral ABEL test_vectors ([A, B] -> [A_EQ_B, A_LT_B, A_GT_B]) [0, 0] -> [1, 0, 0]; [2, 5] -> [0, 1, 0]; [10, 12] -> [0, 1, 0]; [7, 8] -> [0, 1, 0]; [4, 2] -> [0, 0, 1]; [6, 6] -> [1, 0, 0]; [1, 7] -> [0, 1, 0]; [5, 13] -> [0, 1, 0]; [12, 0] -> [0, 0, 1]; [6, 3] -> [0, 0, 1]; [9, 9] -> [1, 0, 0]; [12, 13] -> [0, 1, 0]; [7, 0] -> [0, 0, 1]; [4, 1] -> [0, 0, 1]; [3, 2] -> [0, 0, 1]; [15, 15] -> [1, 0, 0]; END