Question

design a 4 bit comparator that compares two numbers of 4 bits. the output should be < > or =. however you're only limited to using multiplexers or full adders. any help on how to draw this will be appreciated

Answer 1

Ao Ai Bo Bi οημι.cy | 巨 ん(KB) all the CoMespondinq bi

ektivy the ל.cso(a-de ahap.mb. 3fue E- -) L=1

The truth table of the 4bit comparator is given below

OUTPUT COMPARING INPUTS A>B A< B A3> B3 A3 〈 B3 H High Voltage Level, L Low Voltage, Level, X Don't Care

АЗ x3 B3-一 A2 x2 B2 (A<B) Al xl B1 A0 (A>B) x0 B0 (A=B)
In order to implement the above circuit with fewer gates, we modify the circuit that is shown in the following figure

S1 B3 G7 B2 S2 A B (A GT B) G10 Al B1 A0 BO' S4 S5 A2 B2 (AEQU B) Al Bl во G11 B3 G12 G1 A<B (A LT_B) B2 G13 A1' B1 G14 AO B0

In order to reduce the area, we can still decrease the number of gates. The logic of A<B can be decided by A>B and A=B, so we can simplify the above circuit as below. 2-input NOR is used here to realize the function of A<B.The area of 2-input NOR is much less than that of G11~G15. On the other hand, fewer gates means fewer power, so this modification can greatly reduce the power dissipation. Therefore, the logic optimization is completed.

B3 SI G7 S2 G10 Al Bl (A GT_B) S3 A0 во G9 S4 B3 S5 SSi (A LS B) B2 A-B (AEQU B) Al Bl SS2 30