There are multiple schemes that can be used to represent integers in binary, including 1. Assuming that we use 12 bits to represent a number in two's complement scheme, answer the following questions: (a) What are the largest and smallest integers that can be represented? (b) How many different values can be represented? (c) How to represent 2710? (d) How to represent -4510 if supported?
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The range of 2's complement number is { -2n-1 to +2n-1 - 1 } where n is the number of bits.
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- Consider a 6-bit two’s complement representation. Fill in the box with question mark "?" in the following table. You don't need to care about "n/a." Number Binary Representation TMin + TMin ? Please input the binary representation in this format xxxxxx. For example, if the answer is 010010, please input 010010.Suppose A = +54 and B = -3 (both in base 10).Q1: What is the lowest number of rounds theoretically to complete the integer division using the optimized division algorithm?Q2: What is the resulting number in binary representation if we use 8 bits to represent it?Q3: What is the resulting number in FP decimal representation if we use the IEEE 754 standard for single precision? (form of this result should be in sign, true exponent in binary, IEEE-754 Exponent in binary and IEEE-754 exponent in decimal (base 10 number) )Using a "word" of 4 bits, list all of the possible signed binary numbers and their decimal equivalents that are representable in: a) Unsigned integer, b) Signed magnitude, c) One’s complement, d) Two's complementBinary Unsigned IntegerSigned MagnitudeOne’sComplementTwo’s Complement0000000100100011010001010110011110001001101010111100110111101111
- If an unsigned 8-bit integer were to be extended to a 16-bit one, the first 8 most significant bits (MSB) would be filled with ones, creating a signed 16-bit representation. Pick a solution from these two options: Is it true or false that...?What is the number of bits needed to represent the double of a number represented in 5 bits in the binary system? Please Show working out - in stepsIn an 8-bit binary number, which is the most significant bit (MSB)? What is the decimal representation of each of the following unsigned binary integers? 00110101 b. 10010110 c. 11001100 What is the sum of each pair of binary integers? 10101111 + 11011011 10010111 + 11111111 01110101 + 10101100 Calculate binary 00001101 minus 00000111. How many bits are used by each of the following data types? word doubleword quadword double quadword What is the minimum number of binary bits needed to represent each of the following unsigned decimal integers? 4095 65534 42319 What is the hexadecimal representation of each of the following binary numbers? 0011 0101 1101 1010 1100 1110 1010 0011 1111 1110 1101 1011 What is the binary representation of the following hexadecimal numbers? 0126F9D4 6ACDFA95 F69BDC2A Whatistheunsigneddecimalrepresentationofeachofthefollowinghexadecimalintegers? 3A 1BF 1001…
- Consider the following floating point representation where each number has 2exponent bits and 5 fraction bits. The exponent bias is 1. Round each number tohave 3 fraction bits. Apply round-to-even and round-toward-zero modes.a. 1 10 11100b. 0 00 00101c. 1 01 10101i. Can you see a pattern for rounding floating point numbers when thenumber of exponent bits are intact?. Convert 168 and 123 to binary and then compute their addition. How many bytes does it take to represent each number? How many bytes are needed for the answer?Solve all parts or i will dislike A) 1.0 x 2^127 is the largest absolute number that can be represented in the 32-bit representation (True/False) For True enter 1 For False enter 0 ? B) 1.0 x 2^200 will be considered as Infinity in the 32-point representation (True/False) ?
- The following is a string of ASCII characters whose bit patterns have been converted intohexadecimal for compactness: 73 F4 E5 76 E5 4A EF 62 73. Of the eight bits in each pairof digits, the leftmost is a parity bit. The remaining bits are the ASCII code.(a) Convert the string to bit form and decode the ASCII.(b) Determine the parity used: odd or even?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 10Show Steps Please 20. Suppose we have just found yet another representation for floating point numbers. Using thisrepresentation, a 12-bit floating point number has 1 bit for the sign of the number, 4 bits forthe exponent and 7 bits for the mantissa, which is normalized as in the Simple Model so thatthe first digit to the right of the radix points must be a 1. Numbers in the exponent are in signed2's complement representation. No bias is used and there are no implied bits. Show therepresentation for the smallest positive number this machine can represent using the followingformat (simply fill in the squares provided). What decimal number does this equate to?