ECE 274 – Digital Logic Homework Assignment 1 Due September 12 (beginning of class) 1.) (5 points) Convert the following binary numbers to decimal numbers: a. 100 b. 1011 c. 0000000000001 d. 111111 e. 101010 2.) (5 points) Convert the following decimal numbers to binary numbers using the divide-by-2 method: a. 9 b. 15 c. 32 d. 140 3.) (5 points) Convert the following hexadecimal numbers to binary: a. FF b. F0A2 c. 0F100 d. 100 4.) (5 points) Define Moore’s Law. 5.) (5 points) Evaluate the Boolean equation F = (a AND b) OR c OR d for the given values of variables a, b, c, and d: a. a=1, b=1, c=1, d=0 b. a=0, b=1, c=1, d=0 c. a=1, b=1, c=0, d=0 d. a=1, b=0, c=1, d=1 6.) (5 points) Convert each of the following equations directly to gate-level circuits: a. F = ab’ + bc + c’ b. F = ab + b’c’d’ c. F = ((a + b’) * (c’ + d)) + (c + d + e’) 7.) (5 points) Let variables S represent a package being small, H being heavy, and E being expensive. Let’s consider a package that is not small as big, not heavy as light, and not expensive as inexpensive. Write a Boolean equation to represent the following: a. You can deliver packages only if the packages are either small and expensive, or big and inexpensive.b. You can NOT deliver a package that is listed above. Use algebra to simplify the equation to sum of products. c. You can load the packages into your truck only if the packages are small and light, small and heavy, or big and light. Simplify the equation. d. You can NOT load the packages described above. Simplify to sum of products. 8.) (5 points) Use DeMorgan’s Law to find the inverse of the following equation: F = abc + a’b. 9.) (5 points) Convert the function F shown in the following truth table to an equation. Don’t minimize the equation. a b c F 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 10.) (5 points) Determine whether the Boolean functions F = (a + b)’*a and G = a + b’ are equivalent, using: (a) algebraic manipulation, and (b) truth tables. 11.) (10 points) A museum has three rooms, each with a motion sensor (m0, m1, and m2) that outputs 1 when motion is detected. At night, the only person in the museum is one security guard who walks from room to room. Using the combinational design process, create a circuit that sounds an alarm (by setting an output A to 1) if motion is ever detected in more than one room at a time (i.e., in two or three rooms), meaning there must be an intruder or intruders in the museum. Start with a truth table. 12.) (15 points) Consider the museum security alarm function of the previous exercise, but for a museum with 10 rooms. A truth table is not a good starting point (too many rows), nor is an equation describing when the alarm should sound (too many terms). However, the inverse of the alarm function can be straightforwardly captured as an equation. Design the circuit for the 10 room security system, by designing the inverse of the function, and then just adding an inverter before the circuit’s output. 13.) (10 points) A car has a fuel-level detector that outputs the current fuel-level as a 3-bit binary number, with 000 meaning empty and 111 meaning full. Using the combinational design process, create a circuit that illuminates a “low fuel” indicator light (by setting an output L to 1) when the fuel level drops below level 3. 14.) (5 points) Create a circuit that rings a bell whenever motion is detected from one of two motion sensors. A switch S determines which sensor to pay attention to: S=0 means ring the bell when there’s motion at motion sensor 1, S=1 means motion sensor 2. 15.) (10 points) Design a 16x1 multiplexer using AND, OR and NOT
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