1. ) Derive the even-parity Hamming code that corresponds to the following data bits. Be sure to show your work and illustrate how each parity bit was determined. Ob10111000101110
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- Generate the parity bits and longitudinal parity bits for even parity for the characters 01010100, 11100010, 10101110, 11111101, and 00001101.For problems 8, 9 and 10, convert the following decimal numbers into 8‑bit binary numbers as required for 2's complement math, and perform the indicated operations. Circle or bold your binary answer and show your work. 8‑bit binary 2's complement 8 Bits 7 6 5 4 3 2 1 0 21 22 21+22 9 21 -22 21-22 10 -21 22 -21+22Please explain step by step:Let e = 2.71828183 be the Euler’s number with 8 decimal digits of precision.Find the binary scientific notation of e with five bits after the binary point; i.e. find integer n and bits x1, x2, . . . , x5 such that e = 1.x1x2x3x4x5 × 2 n .Find the single-precision IEEE 754 representation of e. (Hint: Round the result of 223e to the closest integer like m. Convert m to its normalized binary scientific notation and round its fraction to 23 bits after the binary point. Finally, find the normalized binary scientific notation of m/2 23 by subtracting 23 from the power of two in the representation of m).
- Assume numbers are represented in 8-bit twos complement representation. Show the calculation of 11000011 - 11101000. It's 195 minus 232, but I don't get how to solve it when the second number is a higher value than the first. How do I subtract this?Suppose the following Hamming Codes were created using even parity, determine if the code is correct or not. If not correct, find the correct Hamming Code. c.) 010101100011Suppose the following Hamming Codes were created using even parity, determine if the code is correct or not. If not correct, find the correct Hamming Code. 2.) 010101100011
- Using 32-bit IEEE 754 single precision floating point with one(1) sign bit, eight (8) exponent bits and twenty three (23) mantissa bits, show the representation of -11/16 (-0.6875).Assuming we are using the Hamming algorithm presented in your text and even parity to design an error-correcting code, find the code word to represent the 8-bit information word 11011011.In error-correcting codes, what is meant by a perfect code? Hence, by using the examples of a (25, 16) Rectangular code and a (15, 11) Hamming code respectively, explain with reasons, whether either of these is a perfect code.
- Perform the arithmetic operations (36)10+(-41)10 and (-1F)16(-2D)16 in .A binary using 12-bit signed-2's complement representation for negative numbers. Convert the answers back to decimal and verify that they are correct Convert the decimal number to single precision IEEE 754 floating-point .B .representation. Show all your workGiven a floating point representation 10110 11101101000 (5-bit exponent and 11-bit significant) 3. if the exponent is in signed magnitude and the significant is in two’s, what are its normalized floating point representation in hexadecimal and its real value in hexadecimal?Perform the arithmetic operations (+70) + (+80) and (−70) + (−80) with binary numbers in signed-2ʹs complement representation. Use eight bits to accommodate each number together with its sign. Show that overflow occurs in both cases, that the last two carries are unequal, and that there is a sign reversal.