![]() ![]() And the third adder adds the result of the second adder to D, and so on for any number of inputs. If E 0, the counter is disabled and remains at its present count even though clock pulse is applied to the flip-flops. An enable input E determines whether the counter is on or off. 1 Up - Down Counter with Enable Design, construct, and simulate a 2-bit counter that counts up and down. The second adder adds the result of the first adder to C. EngineeringComputer EngineeringDesign Problem No. Y = ((A AND B) OR (A AND C) OR (A AND D) OR (B AND C) OR (B AND D) OR (C AND D)) AND NOT XĪs an alternate to what is described above, this function could also be constructed by cascading a two bit adder and two three bit adders. The Y term may be written as all combinations of two inputs being on except when all four are on. 1 when at least two of ABCD are on but not when all four are on. ![]() The function for the Y output is a little less obvious. An odd parity function is easily implemented using XOR gates. We see plainly that the Z output only 1 when an odd number of bits are 1. The truth table for the function looks like.įrom the truth table we see plainly that the X output is only 1 when all bits in ABCD are 1. Let X be the most siginfiant bit of the binary number and let Z be the least significant bit. Given inputs A, B, C, D and outputs X, Y, Z, where XYZ is a 3 bit unsigned binary number representing the number of bits in ABCD that are 1. All these components would not even fit in the available area for the puzzle solution. Representing this in the puzzle would require 6 4-way ANDs, 1 4-way OR, and 3 2-way ORs. Which has the following expression: A'B'CD + A'BD + ABC' + AB'D + BCD' + AB'CD' For example, for the second output column, I got the following Karnaugh map: I tried solving this using a Karnaugh map, but it is still resulting in an expression that is way too big for the puzzle solution area. The truth table for a 4-bit bit counter looks like this (inputs on left, output on right): If you try to write that all out and simplify it, it will be very complex and a lot of opportunity for making errors. This is a 16-row truth table with 3 columns of outputs. In each state there are two possible inputs, one for Up and one for Down. Note: figuring out how to do this is not easy. To design a two-bit up-down counter that skips the count (decimal base 2). Is there any book that COMPREHENSIVELY describes the construction of all common combinatorial circuits, such as bit counters, adders, etc, using basic logic gates? I find it extremely frustrating that making basic combinatorial logic circuits is some kind of black voodoo that is undocumented. Nowhere in this book does it tell how to make a bit counter out of logic gates. I also have the book Hill & Horowitz, used to teach digital logic. My code increments the z output once and then stops at 01 when I simulate it in Vivado 2017. I bought a book called "Digital Principles" by Schaum's Outlines and nowhere in this book does it tell how to make a bit counter out of logic gates. Design and simulate a 2-bit counter which after a reset counts 00, 01,10, 11, 00, 01. So, for example, the value '1011' would have the result '011' because three bits are set and '011' means 3 in binary. A bit counter tells how many bits are set in a value. I cannot figure out a puzzle which is to create a 4-bit bit counter using basic logic gates (NOT, OR, AND, NOR, NAND, XOR, XNOR, MUX, FULL ADDER). ![]()
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