Express the value 0.3 in the 32-bit floating point format that we discussed in class today. Feel free to only show fraction bits [22:15], rather than all the fraction bits. [22:0]. Notation: The symbol [22:15] signifies all 8 bits from bit 22 to bit 15.
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- VI. Floating point representation Consider a 12-bit variant of the IEEE floating point format as follows: • Sign bit 5-bit exponent with a bias of 15. • 6-bit significand All of the rules for IEEE 754 Standard apply. Fill in the numeric value represented by the following bit patterns. You must write your number in decimal form (e.g. 0.0146485375, -0.0146485375). Bit Pattern 010011101110 111011101011 100101001111 001010111010 Numerical Value4. The bfloat16 "brain floating point" format is a 16 bit format used in Google's machine learning and AI software. It is a binary floating point format which is very similar to the single precision IEEE-754 format: 1 bit is allocated for the sign, 8 bits for the exponent with a bias of 127, but only 7 bits are allocated for the fraction (the exponent is always chosen so that the first digit of the mantissa is 1, and then only the fraction is stored in memory). (a) What is the approximate decimal precision of a brain floating point? (b) If the bits are stored in the order: sign, exponent, fraction, and 0 corresponds to a positive sign, then calculate the decimal representation of the number stored as 1 00000110 0100010 (c) Given that the largest exponent actually used for numbers is 11111110, what is the largest number that can be expressed as a bfloat 16? (d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?4. Floating Point Arithmetic Give the answer (in traditional decimal or scientific notation) to the computations below. Each number in binary represents a IEEE single precision number, broken up into the 3 groups of sign, exponent and significand. 1.5+ (1 01111110 10000000000000000000000 ) = (0 10000011 00000000000000000000000) / 4 =
- a) Write IEEE floating point representation of the decimal number 3.14 (show work). (First, you need to convert it to binary equivalent. Compute only 4 bits after the binary point) b) Write the decimal equivalents for the following IEEE floating point number (show work). 110000011000100100000000000000003. On a computer, floating-point numbers are represented in the following way t e u m t = sign of exponent, 1 bit e absolute value of exponent, 3 bits FLOATING-POINT ARITHMETIC u= sign of mantissa, 1 bit m = mantissa, 5 bits The base is 2 and the mantissa is normalized. (a) Give the largest number that can be represented exactly. (b) Determine the decimal number corresponding to the word (0101010110) 2. 27Assignment for Computer Architecture! this is about hamming codes write the code IN MIPS ASSEMBLY LANGUAGE calculating hamming codes; The key to the Hamming Code is the use of extra parity bits to allow the identification of a single error. Create the code word as follows: Mark all bit positions that are powers of two as parity bits. (positions 1, 2, 4, 8, 16, 32, 64, etc.) All other bit positions are for the data to be encoded. (positions 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, etc.) Each parity bit calculates the parity for some of the bits in the code word. The position of the parity bit determines the sequence of bits that it alternately checks and skips.Position 1: check 1 bit, skip 1 bit, check 1 bit, skip 1 bit, etc. (1,3,5,7,9,11,13,15,...)Position 2: check 2 bits, skip 2 bits, check 2 bits, skip 2 bits, etc. (2,3,6,7,10,11,14,15,...)Position 4: check 4 bits, skip 4 bits, check 4 bits, skip 4 bits, etc. (4,5,6,7,12,13,14,15,20,21,22,23,...)Position 8: check 8 bits,…
- II. Assume we are running code on a 10-bit machine using two's complement arithmetic for signed integers. Fill in the empty boxes in the table below. The following definitions are used in the table: int y = -9; unsigned z = y; Note: You need not fill in entries marked with Only accepted format for binary representation (use 10-bits): 0000000000, 1111111111 Only accepted format for hexadecimal representation: 2FD, 1EF, 3FF Expression Decimal Binary Hexadecimal Zero 0 -5 y Z y-z -Tmax -Tmin Tmax +1 00000100104. The largest number with two-byte word length is: Ans: 5. How many lines needed in parallel representation to transimmit decimal integer values up to 17 in binary. Ans: is (2), -Q₁. 6. The base of the following is Ans:There are 2 numbers, X and Y in single-precision floating point representations. X=45B20000 and Y=B66C0000. Perform the multiplication operation on the two numbers using the floating-point number multiplication algorithm (the result is still in the floating-point format). Then convert each of them: X, Y and the results to a decimal number (fixed point).
- A barcode scanner for Universal Product Codes (UPCS) verifies the 12-digit code scanned by comparing the code's largest digit (called a check digit) to its own computation of the check digit from the first 11 digits as follows: 1. Calculate the sum of the digits in the odd-numbered positions (the first, third,. eleventh digits) and multiply this sum by 3. 2. Calculate the sum of the digits in the even-numbered position (the second, fourth...tenth digits) and add this to the previous result. 3. If the last digit of the result from step 2 is 0, then 0 is the check digit. Otherwise, subtract the last digit from 10 to calculate the check digit. 4. If the check digit matches the final digit of the 12-digit UPC, the UPC is assumed correct By using C++ write a program that prompts the user to enter the 12 digits of a barcode separated by space. The program should store the digits in an integer array, calculate the check digit, and compare it to the final barcode digit. If the digits match,…Assume we are using the simple model for floating-point representation discussed in the class (the representation uses a 14-bit format, 5 bits for the exponent with an Excess-M, a significand of 8 bits, and a single sign bit for the number): Convert 12.345 to the floating-point binary representation. (Remember we learned "implied one" format in the lecture) You need to type in the calculation steps or insert the picture of your handwriting using "insert" menu above.Q. Write binary codes for the following words as per ASCII coding scheme. 1) Don't 2) ASCII8 ASCII Code: Character to Binary 0011 0000 0100 1111 0110 1101 1. 0011 0001 P 0101 0000 0110 1110 2 0011 0010 0101 0001 0110 1111 3 0011 0011 0101 0010 0111 0000 4 0011 0100 0101 0011 0111 0001 0011 0101 0101 0100 0111 0010 6 0011 0110 0101 0101 0111 0011 0011 0111 V 0101 0110 t 0111 0100 0011 1000 0101 0111 0111 0101 9 0011 1001 0101 1000 0111 0110 0100 0001 0101 1001 0111 0111 0100 0010 0101 1010 0111 1000 0100 0011 a. 0110 0001 0111 1001 0100 0100 b 0110 0010 0111 1010 E 0100 0101 0110 0011 0010 1110 0100 0110 0110 0100 0010 0111 0100 0111 e 0110 0101 0011 1010 H. 0100 1000 0110 0110 0011 1011 0100 1001 0110 0111 0011 1111 0100 1010 0110 1000 0010 0001 K 0100 1011 0110 1001 0010 1100 L 0100 1100 0110 1010 0010 0010 M 0100 1101 k 0110 1011 0010 1000 0100 1110 1. 0110 1100 0010 1001 space 0010 0000