What is the most important concept in converting any number from Base m to Base n
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- The following is an addition problem displayed in standard base 10 notation. Each letter represents a different digit (each digit must be an integer in the range of 1 to 9). What digit does each letter represent? What information did you use to get started with narrowing down possible values for the letters? PXQ + XYX ----- QXQY5. What are the decimal equivalents of the following hexadecimal numbers? 336699; FFCC22 ; 345678; 999999; 000000;What is the decimal equivalent of the given code?
- Some people argue that many of our calculations would be easier in the base 12 numbersystem because 12 is divisible by so many more numbers than 10 (for base 10). What is the lowestdigit in base 12? What would be the highest symbol for the digit in base 12? What are the positionalvalues of the rightmost four positions of any number in the base 12 number system?2. How many even 4-digit numbers greater than 3000 can be formed from the digits 2, 6, 7, 8, 9 if no digit can be used more than once?What is the length of a double-precision integer under the IEEE-754 floating-point standard?
- The Famous Gauss You must know about Gauss, the famous mathematician. Back in late 1700’s, he was at elementary school. Gauss was asked to find the sum of the numbers from 1 to 100. The question was assigned as “busy work” by the teacher. He amazed his teacher with how quickly he found the sum of the integers from 1 to 100 to be 5050. Gauss recognized he had fifty pairs of numbers when he added the first and last number in the series, the second and second-last number in the series, and so on. For example:(1 + 100), (2 + 99), (3 + 98), ..., (50 + 51). Each pair has a sum of 101 and there are 50 pairs. History repeats itself. Jojo’s teacher assign a “busy work” to the students. The teacher believes that there will be no shortcut to finish this task in a minute. The teacher gives N integers A1, A2, ..., AN to the students. The teacher also gives Q questions. Each question contains two integers L and R asking the sum of all Ai where L <= Ai <= R. As a good friend of Jojo, help Jojo…What are the advantages of floating-point numbers over integers?What are the three pieces that make up a floating-point number and how do they work together?
- What is the smallest positive number that can be represented in IEEE single precision floating point? You can express your answer as a significand times a base raised to a power.The following is a multiplication problem in traditional base ten notation. Each letter represents a different digit. What digit does each letter represent? How did you get your foot in the door? XY*YX=XY*YZ=WVYWhat is the 58th decimal digit in the decimal representation of 9/11=