iii) Compute 103 + 50, 103-50,-103 +50,-103.50. (14%) 4) Integer multiplication.
ID: 3872507 • Letter: I
Question
iii) Compute 103 + 50, 103-50,-103 +50,-103.50. (14%) 4) Integer multiplication. Multiply 103 (multiplicand) by 5 (multiplier), and -5 Cu (multiplicand) by 7 (multiplier). The results are stored in 16-bit words. Use the way 3 we multiply two decimal numbers on the paper to muktiply these binary numbers. (1 8%). 5) Represent 2.366 in the IEEE 753 32-bit floating point format. Round up/down the significand, keeping only 6 numbers of the significand. (10%). 6) Convert the following IEEE 754 binary number into a decimal number: Sign bit: 0: exponent: 100000101; fraction: 1000 1000 0 (10%) 7) Compute the addition and multiplication of the following 2 binary floating numbers. Hint: addition: alignment, addition, normalization, rounding; multiplication: addition of exponent, multiplication of significands, normalizati and rounding. Keep only 5 numbers of the s and show the result in normalized format (18%). 1.101 * 21 and 1.1 * 2-1Explanation / Answer
Here in 5 & 6 Both are same where as in 5 we are representing the decial number in IEEE 754 32 bit format and in 6 we are binary number into decimal number using IEEE 754.
IEEE Standard 754 floating point is the most common representation today for real numbers on computers, including Intel-based PC's, Macintoshes, and most Unix platforms
Single: SEEEEEEE EMMMMMMM MMMMMMMM MMMMMMMM
Double: SEEEEEEE EEEEMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM MMMMMMMM
The Sign Bit
The sign bit is as simple as it gets. 0 denotes a positive number, and 1 denotes a negative number. Flipping the value of this bit flips the sign of the number.
a. The sign bit is 0 for positive, 1 for negative.
b. The exponent base is two.
c. The exponent field contains 127 plus the true exponent for single-precision, or 1023 plus the true exponent for double precision.
d. The first bit of the mantissa is typically assumed to be 1.f, where f is the field of fraction bits.
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