34 Lecture - Number Systems and Radix Conversion

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34 Lecture

CS501

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Number Systems and Radix Conversion

Number systems refer to the different ways of representing numerical values using symbols or digits. The most common number systems are the decimal, binary, octal, and hexadecimal systems. Radix conversion is the process of converting a number f


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  1. What is the base of the binary number system? A. 8 B. 10 C. 2 D. 16 Answer: C What is the base of the octal number system? A. 2 B. 8 C. 10 D. 16 Answer: B What is the base of the hexadecimal number system? A. 2 B. 8 C. 10 D. 16 Answer: D What is the decimal equivalent of the binary number 1010? A. 8 B. 10 C. 12 D. 16 Answer: C What is the decimal equivalent of the octal number 63? A. 51 B. 54 C. 57 D. 60 Answer: D What is the binary equivalent of the decimal number 29? A. 11101 B. 10111 C. 10011 D. 11001 Answer: A What is the octal equivalent of the decimal number 95? A. 137 B. 147 C. 157 D. 167 Answer: B What is the hexadecimal equivalent of the binary number 1110101? A. 4D B. 5D C. 6D D. 7D Answer: A What is the decimal equivalent of the hexadecimal number 2A? A. 38 B. 40 C. 42 D. 44 Answer: C What is the binary equivalent of the octal number 53? A. 100101 B. 101010 C. 110001 D. 111000 Answer: C



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  1. What is a number system? Answer: A number system is a way of representing numerical values using symbols or digits. What is radix conversion? Answer: Radix conversion is the process of converting a number from one number system to another. What is the decimal equivalent of the binary number 1101? Answer: The decimal equivalent of the binary number 1101 is 13. What is the binary equivalent of the decimal number 25? Answer: The binary equivalent of the decimal number 25 is 11001. What is the octal equivalent of the binary number 101101? Answer: The octal equivalent of the binary number 101101 is 55. What is the hexadecimal equivalent of the binary number 111001? Answer: The hexadecimal equivalent of the binary number 111001 is 39. What is the decimal equivalent of the octal number 75? Answer: The decimal equivalent of the octal number 75 is 61. What is the octal equivalent of the decimal number 83? Answer: The octal equivalent of the decimal number 83 is 123. What is the binary equivalent of the hexadecimal number 2F? Answer: The binary equivalent of the hexadecimal number 2F is 101111. What is the hexadecimal equivalent of the octal number 67? Answer: The hexadecimal equivalent of the octal number 67 is 2F.

Number systems are used to represent numerical values using symbols or digits. The most commonly used number systems are the decimal system, binary system, octal system, and hexadecimal system. The decimal system is the base-10 number system, which uses 10 digits (0-9) to represent values. The binary system is the base-2 number system, which uses two digits (0 and 1) to represent values. The octal system is the base-8 number system, which uses eight digits (0-7) to represent values. The hexadecimal system is the base-16 number system, which uses 16 digits (0-9 and A-F) to represent values. Radix conversion is the process of converting a number from one number system to another. This involves dividing the number by the base of the destination number system and converting the remainders to the corresponding symbols. For example, to convert the decimal number 25 to binary, we can divide it by 2, which gives a quotient of 12 and a remainder of 1. We then divide 12 by 2, which gives a quotient of 6 and a remainder of 0. We continue this process until we get a quotient of 1 and a remainder of 1. The remainders, read from bottom to top, give us the binary equivalent of 25, which is 11001. Similarly, to convert the binary number 101101 to octal, we can group the digits into groups of three, starting from the right. We then convert each group to its decimal equivalent and write down the corresponding octal symbols. In this case, we have 101 101, which is equivalent to 5 5 in octal. Radix conversion can also be used to convert numbers from one base to another. For example, to convert the hexadecimal number 2F to binary, we can convert each hexadecimal digit to its binary equivalent. In this case, 2 is equivalent to 0010 and F is equivalent to 1111. Putting these together, we get the binary equivalent of 2F, which is 00101111. Overall, number systems and radix conversion are important concepts in computer science and are used extensively in digital electronics, computer programming, and data storage and retrieval systems.

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