Computing Machinery II Assignment 1 Solution

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Description

Combinational Logic: Binary-to-Seven-Segment Decoder

A seven-segment display consists of seven individual segments that can be turned off or on in particular combinations to display digits and a limited number of alphabetic characters. The arrangement and labelling of the segments are shown below:

lu2384l32831 tmp c12c34f267b85b05

The digits 0 to 9 and the letters A to F can be displayed as shown:

lu2384l32831 tmp a8474282d746dc57 lu2384l32831 tmp b4dedf68e92fc368 lu2384l32831 tmp 98bdfa583b17ba6 lu2384l32831 tmp ef7981b716836a16 lu2384l32831 tmp 8b5fe6cc451999cf lu2384l32831 tmp 8fd675bf493db61c lu2384l32831 tmp f7698f2e24ce5afa lu2384l32831 tmp ae9d9334b478a060 lu2384l32831 tmp 7c566d38c37d0c1d lu2384l32831 tmp 6b2d5b38c7b8f881 lu2384l32831 tmp e9a3500175bd1621 lu2384l32831 tmp ed2ac372799939f2 lu2384l32831 tmp d2f1c886a1026f9c lu2384l32831 tmp 8d85377a2627e5f8 lu2384l32831 tmp 69242baddc0fa7ac lu2384l32831 tmp 9315da0503f9a5ea

Design a combinational logic circuit that takes a 4-bit number as an input (that is, a binary number ranging from 0000 to 1111) and produces 7 outputs, one each for the 7 segments of the display unit, to show the corresponding hexadecimal number. Assume that 0 means off and 1 means on. Use the design method outlined in class, and create a report showing all steps:

  1. State the problem in words.

  2. Determine the input and output variables.

  3. Assign letter symbols to the variables.

  4. Create the truth table that defines the relationships between inputs and outputs.

  5. Obtain the simplified function for each output (show all steps for this, whether done algebraically or using the map method).

  6. Implement the functions using the appropriate gates (show a logic diagram for this).

This report should be printed out and submitted on paper. Your diagrams and tables can be hand written or created using a graphics program.

Circuit Simulation

Implement your design in the Logisim application, using the 7-Segment Display as output. This display also includes an input for a decimal point, which you should ignore (make sure it is always turned off). Arrange things so that the four inputs appear on the left, the decoder circuitry in the middle, the display unit on the right. Save your design in a file called assign1.circ, which will be submitted electronically using D2L.

Bonus (10% if fully implemented)

Add a 4-bit counter to your Logisim circuit to drive the inputs of the decoder. It should cycle through the range 0000 to 1111, and then wrap around to 0000. Arrange this circuit so that the counter increments every time a button is pushed. Save this design in a file called assign1bonus.circ, which will be submitted electronically using D2L.

New Skills Needed for this Assignment:

  • Ability to work with binary logic, Boolean algebra, and logic gates

  • Ability to minimize Boolean functions, either algebraically or by using the map method

  • Ability to design combinational circuits following the prescribed design procedure

Submit the following:

  1. Your report on paper. Submit this using the assignment boxes located on the main floor of the Math Sciences Building (in the main floor Computer Science lab area).

  2. Your Logisim file: assign1.circ (and assign1bonus.circ if doing the bonus) submitted using D2L.

Computing Machinery II

Assignment 1 Grading

Student:__________________________________________

Report

Statement of problem 4 ______

Input and output variables 2 ______

Assign letters to variables 2 ______

Truth table 11 ______

Simplified functions 14 ______

Logic diagram 14 ______

Circuit simulation in Logisim 10 ______

Total 57 ______ _____%

Bonus (10% if fully implemented) _____%

Assignment Grade _____%