Suppose we use six bits to represent a two's complement binary number. (a) What is the largest number that can be represented? (b) What is the smallest number that can be represented? (c) How many total base-10 numbers can be represented?
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- 1.What is the minimum number of binary bits needed to represent each of the following unsigned decimal integers? 4095 65534 42319 2.What is the hexadecimal representation of each of the following binary numbers? 0011 0101 1101 1010 1100 1110 1010 0011 1111 1110 1101 1011 3.What is the binary representation of the following hexadecimal numbers? 0126F9D4 6ACDFA95 F69BDC2A 4.What is the unsigned decimal representation of each of the following hexadecimal integers? 3A 1BF 1001 5.What is the unsigned decimal representation of each of the following hexadecimal integers? 62 4B3 29F1. What is the binary representation of the largest positive integer that can be represented with 19 bits 2. What is the LARGEST base ten number that can be represented with 1 BYTE in Binary4. Fill in the empty slots in the table by converting numbers into different representations. All numbers are 8 bits in length. Use 2's complement representation in binary and hexadecimal numbers. Signed Decimal Binary 0010 0001 1010 0100 Hexadecimal Unsigned Decimal 6F 33 -25
- What are the mantissa and exponent values if 6.75 is represented in 8-bit binary floating-point representation? a) Mantissa is 1011 and exponent is 101 b) Mantissa is 0011 and exponent is 100 c) Mantissa is 1011 and exponent is 100 d) Mantissa is 0011 and exponent is 101Round the following binary numbers (rounding position is bolded – it is the bit at the 2-4 position) following the rounding rules of the IEEE floating point representation. I. 1.00111112 II. 1.10010012 III. 1.01111002 IV. 1.01101002 For each of the four (4) resulting rounded binary numbers, indicate - what type of rounding you performed and - compute the value that is either added to or subtracted from the initial binary number (listed above) as a result of the rounding process. In other words, compute the error introduced by the rounding (approximation) process. please note that the rounding is based on the bolded numbers!!! Not the 2s in the end those are just binary signsWhat decimal value does the 8-bit binary number 10101110 have if: a) it is interpreted as an unsigned number? b) it is on a computer using signed-magnitude representation? c) it is on a computer using one's complement representation? d) it is on a computer using two's complement representation? e) it is on a computer using excess-127 representation?
- 1. Consider the following numbers: 1.44375 x 10¹ and -5.3125 x 10¹. Find their binary representation. Show all the required steps.Convert the following decimal number into equivalent binary number and hence write the binary number in 64- bit long real format (53.36755) i need the answer by same way example through picture please.!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 10
- What decimal value does the 8-bit binary number 10011110have if:1. a) It is interpreted as an unsigned number?b) It is on a computer using signed-magnituderepresentation?2. c) It is on a computer using one’s complementrepresentation?3. d) It is on a computer using two’s complementrepresentation?4. e) It is on a computer using excess-127 representation?1. Two's complement notation really shows its value in binary addition, where positive and negative quantities may be handled with equal ease. Add the following byte-long (8 bit) two's complement numbers together, and then convert all binary quantities into decimal form to verify the accuracy of the addition: (show Work) a. 00110101 +00001100 00001010 +10010101 01110110 +00000010 11111110 +11011101 00111101 +11111011 11111110 +1111110113. Convert each decimal number to binary using repeated division by 2: (b) 21 (c) 28 (d) 34 (е) 40 (f) 59 (g) 65 (h) 73 14. Convert each decimal fraction to binary using repeated multiplication by 2: (a) 0.98 (b) 0.347 (c) 0.9028 TION 2-4 Binary Arithmetic 15. Add the binary numbers: (a) 11 + 01 (b) 10 + 10 (c) 101 + 11 (d) 111 + 110 (e) 1001 + 101 (f) 1101 + 1011