Example: Construct a Huffman's code for symbol below: x = [X1, X2, X3, X4, X5, X6] with corresponding probabilities are p(x) = [0.3, 0.25, 0.2, 0.1, 0.1, 0.05], then calculate the coding efficiency.

Computer architecture  1. Perform the following calculations. All numbers are 8-bit Integers; except where noted. Show all work. Note any overflow. Note that 2c signifies 2s complement and sm signifies signed-magnitude. I suggest you check your answers in base 10. 11110110 - 100101112c= 11110110 & 00001111= Convert -1610sm to Base 16 Convert AD16c to Base 10 F9 + E916c=

Excess-3 code is significant for arithmetic operations as it overcomes shortcoming encountered while using 8421 BCD code to add two decimal digits whose sum exceeds 9. Excess-3 arithmetic uses different algorithm than normal non-biased BCD or binary positional number system.  An electronics company has hired your services to design a code converter that converts Binary Coded Decimal (BCD) code for it. Design the converter.

1. Gray code to Binary converter: Gray code is one of the codes used in digital systems. It has the advantage over binary numbers that only one bit in the code word changes when going from one number to the next. (See Table 1). Design a combinational circuit with 4 inputs and 4 outputs that converts a four- bit gray code number into an equivalent four-bit Binary number. Use Karnaugh map technique for simplification. Use LogicWorks for pre-lab demonstrations. Select the library "7400dev.clf* in the Parts Palette and then select the XOR chip 74-86. This would give you a set of 4 XOR's as shown in Fig. 1, just like the hardware chip 74-86. You could use as many as needed from these XOR gates in your design. Get back to ALL LIBRARIES and select switches for the inputs and Binary Probes as indicators of the outputs. Verify your design in the pre-Lab. During the Lab construct the circuit and verify its operations.