Bit Binary Multiplier

Question

Problem 1: 2 Bit Binary Multiplier

We need a circuit that multiplies two 2-bit binary numbers.

Example

                          10₍₂₎                                                                      2 ₍₁₀₎

                        _* 10_{(2)                                                                   *}  2 ₍₁₀₎

                        _{___________________________        =               ___________________________}    

                   0 0                                                              4 ₍₁₀₎

              1 0

_{___________________________}     

100 ₍₂₎

 

Design the logic circuit as directly as possible (i.e. don't try using adder circuits). Turn in your truth table, reduced logic equations, and reduced logic circuit diagrams.

 

 

 

 

 

 

Problem 2: Lawn Mower Logic

Translate the following statements into a truth table, reduce the logical function, and draw the logic circuit diagram.

 

1)    My lawn mower protects me with three switches )read 'switches' as 'inputs'

A)    a seat switch that indicates that I am sitting down

B)    a parking brake switch that indicates that the parking brake is set

C)    a mower switch that tells me the mower is spinning

 

2)    If the mower is on and I am off the seat, the engine dies

3)    If the mower is off and the parking brake is off and I am off the seat, the engine dies

4)    If the mower is off and the parking brake is on and I  am off the seat, the engine keeps running

Turn in your truth table, reduced logic equations, and reduced logic circuits.

Problem 3: Elevator Display

The Why Be Normal Elevator Company (WBNEC) needs a display for its new 'transvator'. The transvator is designed to move both up and down and sideways, so it can deliver you to your office door. The display needs to tell toy what direction you are about to move. The problem is WNMEC insists that you use a standard 7-segment display. (*Hint: You can tilt the display.) Design a decoder that will display up-down-left-right. Turn in the truth table, a sketch of the display, reduced logic equations, and reduced logic circuits. 

Problem 4: Window Comparator 

Design a circuit, a comparator circuit, that outputs a logic '0' if an input voltage is less than one volt or greater than two volts and a logic '1' if an input voltage is between one and two volts.