***Represent the decimal number -6 in binary using 4-bits: 3a) signed magnitude ____________________________ 3b) 1’s complement _____________________________ 3c) 2’s complement _____________________________
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***Represent the decimal number -6 in binary using 4-bits:
3a) signed magnitude ____________________________
3b) 1’s complement _____________________________
3c) 2’s complement _____________________________
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- Complete the following table for a word size of 12 bits UMax (unsigned Max Value) Hex:_______________ Decimal:_______________ TMax (signed Max Value) Hex:_______________ Decimal:_______________ TMin (signed Min Value) Hex:_______________ Decimal:_______________ TMax + 1 Hex:_______________ Decimal:_______________ -1 Hex:_______________ 0 Hex:_______________1. In a binary coded decimal (BCD) system, 4 bits are used to represent a decimal digit from 0 to 9. For example, 3710 is written as 00110111BCD. (a) Write 28910 in BCD (b) Convert 100101010001BCD to decimal (c) Convert 01101001BCD to binary (d) Explain why BCD might be a useful way to represent numbersPerform the following base conversions:1. a) 21200 = _________102. b) 3244 = _________103. c) 3402 = _________104. d) 7657 = _________10
- Convert IEEE Single-Precision Binary Format Real number 11000100101001000010101000000000 to decimal. Please show all the steps. a) [1] What is the sign? b) [1] What is the biased exponent value? c) [1] What is the unbiased exponent value? d) [2] What is the normalized representation of the number in BINARY? e) [1] What is the unnormalized representation of the number in BINARY? f) [1] What is the decimal value of the whole number part of the number? g) [2] What is the decimal value of the fractional part of the number? h) [1] What is the real number in base 10H - For the IEEE 754 single-precision floating point, write the hexadecimal representation for the following decimal values: (i)–1.0 (ii)– 0.0 (iii)256.0156259)The following numbers use the IEEE 32-bit floating-point format. What is the equivalent decimal value? (a) 1 10000011 11000000000000000000000 (b) 0 01111110 10100000000000000000000 (c) 0 10000000 00000000000000000000000
- Question 11 Not yet answered P Flag question A computer system uses 8 bits to represent floating-point values. The 8 bits are organised as follows: The first bit is a sign bit (0 for positive, 1 for negative). The middle 3 bits are the exponent, which uses bias of 3. The last 4 bits are the significand, which is normalised in the same way as the significand is normalised in IEEE-754 formats. The format does not reserve any special values. The following arithmetic operation is performed on this system: 00011000 x 11000110 The result is then stored in the same 8-bit floating-point format. What is the relative error of the stored result comapred to the value of the result of the arithmetic operation? Answer s are rounded to 5 decimal places. O a. None of the other answers. O b. 0.03030% O c. 0.03125% O d. 0.97865% O e. 0%4. 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?dont use others answers 3 a) Represent the decimal number -89 in binary using 8-bit: i.Signed magnitude: ____________________________ ii.One's complement: ____________________________ iii.Two's complement: ___________________________ b) What decimal value does the 8-bit binary number 10011110 have if: i.it is interpreted as an unsigned number? ___________________________ ii.it is on a computer using signed-magnitude representation? _______________________ iii.it is on a computer using one’s complement representation? _______________________ iv.it is on a computer using two’s complement representation? _______________________
- TMin - 1 (write in decimal representation): -TMin: -TMax: TMAX> AGiven the following decimal numbers 15.0625, -35.6875, 86.5625, and 0.125, represent them in IEEE 754 binary representations in single precision float.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.