CSCE 211 Digital Logic Analysis and Design

Circuit 2

Design Problem Using K-Maps

Design a logic circuit whose input is a binary-coded decimal number (4 bits) and whose output detects BCD codes strictly less than 7. For binary-coded decimal, the codes 10-15 are don't cares. Your circuit board should have the following buffer-driven (inverter-driven) LED circuits, each of which uses a gate from the 74LS05 hex-inverter chip:

• 4 LED circuits for the input signals (A, B, C, D) from Circuit No. 1. A is the most significant bit of the 4-bit code. Don’t confuse the variables names B, C, and D. with the abbreviation for binary-coded decimal (BCD)!
• 1 LED circuit for F(A, B, C, D), the output signal. The “floating” pin (1) of the 74LS05 is used to display the value of F.

Use a K-map to simplify the design. Use a NAND-NAND implementation (sum of products). You will need a 74LS10 (3-input NAND) and 74LS04 (hex-inverter). Diagrams for 74xx series integrated circuits. Place the new chips with the notch pointing to the battery pack; don’t forget to connect Vcc and GND to them.

Draw the circuit on paper before you build it—that is, specify pin numbers before you start making connections. Please use the drawing template provided in your kit.

A deduction of 25 points will be made if the circuit is drawn without using the template or drawing program.

As shown in class, the function is easy to design if we simplify F′ and then invert it back to F with an inverter from the 74LS04 chip. The function output is connected to the
F(A, B, C, D)-LED circuit. The 74LS04 and 74LS05 inverters do not cancel each other. The 74LS05 is still needed to provide power (“drive”) the F(A, B, C, D)-LED.

Check-off: Demonstrate that your circuit output is correct for all input combinations.

Report: Your short report must include the following:

• The K-map simplification of the function.
• The logic diagram. Label the inputs as A, B, C, D, where A is the most significant bit of the binary-coded decimal number.
• Please be sure to include physical wiring information—gate ID and pin numbers—on the logic diagram.

Design Hints

• Get the big picture first: inputs to a function; single output
• Specify the function with a truth table and draw the K-map
• Simplify the K-mao.
• Draw the logic diagram and identify needed gates (label them).
• Add wiring information to logic diagram. Examples:
  • From signal A to inverter #1 input [pin(1)]
  • From inverter #1 output [pin(2)] to NAND gate #1 input [pin(4)]
• Place parts on protoboard and make the connections
• Remember: Trust nothing. Test everything.