. Represent the following two integers (2 bytes each using 2's complement) in computer memory (Hex representation): 41, -23, i. Represent the following word in memory (8-bit ASCII chars using even parity) : big
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- Perform the following additions and subtractions. Assume the numbers are stored in hexadecimal representation. (Explain step by step.) a. 74F – D63E1) IEEE 754 Floating Point Standard: This standard is used to represent floating-point numbers (real numbers) digitally in computer memory. The standard provides two representations which have different accuracies: double precision and single precision. > Double Precision – 8bytes = 64 bits o Bit 63 (one bit): Sign (0=positive, 1=negative) o Bits 62 to 52 (11 bits): Exponent, biased by 1023 o Bits 51 to 0 (52 bits): Fraction f of the number 1.f Single Precision – 4bytes = 32 bits o Bit 31 (one bit): Sign (0-positive, 1=negative) o Bits 30 to 23 (8 bits): Exponent, biased by 127 o Bits 22 to 0 (23 bits): Fraction f of the number 1.f Procedure to Find the Double-Precision Representation of a Number x: Let the representation be (b63, b62, ..., b, b,, bo) with b63 being the most-significant bit and bo being the least significant bit. Sign Bit: (0, x20 l1, x1 { set new bit as 1 y + y-1 else set new bit as 0 EE 426 Homework 2 Spring 2020/2021 a) Find the double-precision representation of…5) Determine the 32-bit binary representation for floating point numbers in the form +1. F x be Where, i is the integer part, F is the fraction, b is the base, and e is the exponent. Using this format, represent the number 0.00001011001100101 as a 32 bit floating point number.
- Floating point calculation: a Show the IEEE 754 representation for the decimal value -0.375 in single precision b. Find the decimal representation for the following single precision floating point number 1011,1111,0111,0000,0000,0000,0000,0000 c. Perform the addition and multiplication of the two floating point numbers in (a) and (b) in binary scientific notation, and represent the sum and product in single precision.Answer the following questions on floating-point representation: a) Convert AD510010 16 to an IEEE single-precision floating-point number b) Convert the following IEEE single-precision floating-point number to a decimal number: 10111111110100000000000000000000(2) jla It is guaranteed that a has at least 8 bits and a has at least .16 bits int, float char, int bool, char char, short
- 3. Represent the decimal number 30 in 8-bit binary number using the following representation methods: a) one's complement: b) Excess-M:Assignment 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,…3. Fractional Values Complete the following table. The first row is filled in to show the kind of values expect ed. For simplicity, the bits of the floating point numbers are shown in 3 groups - sign, exponent and significand. For the 8 bit floating point assume 1 bit for the sign bit, 4 for the exponent, and 3 bits for the significand. The bias is 7 for this type. Decimal Binary Fixed Point 8 bit floating point 0.25 0.01 0 0101 000 0.125 1.101 0 1101 100
- 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 ValueExamples of 8-bit binary representations of the decimal value 30 are shown below. definition a) the opposite of a term; b) Excess-M;?c) Find the normalized scientific notation for the following decimal numbers: 1) 1012.88 11) 0.09998 d) In IEE754 single precision format, how many bits are required to store a decimal number 2? Show how it is stored. e) What is the advantage of using the in-excess representation for an exponent? f) Using binary presentation, show the decimal floating values of -6120.3125 in IEEE754 single precision format.