1. Digital systems use a variety of different number systems. The number system is a way ofexpressing numbers. Number system conversions deal with the operations to change the base ofthe numbers.a. Convert the following values into hexadecimal.i. 7348ii. 63548
Question
- Digital systems use a variety of different number systems. The number system is a way ofexpressing numbers. Number system conversions deal with the operations to change the base ofthe numbers.a. Convert the following values into hexadecimal.i. 7348ii. 63548
Solution
To convert the decimal numbers to hexadecimal, you can use the division-remainder method.
i. Convert 7348 to hexadecimal:
- Divide the number by 16. 7348 ÷ 16 = 459, remainder 4. The hexadecimal equivalent of 4 is 4.
- Divide the quotient by 16. 459 ÷ 16 = 28, remainder 11. The hexadecimal equivalent of 11 is B.
- Divide the quotient by 16. 28 ÷ 16 = 1, remainder 12. The hexadecimal equivalent of 12 is C.
- Divide the quotient by 16. 1 ÷ 16 = 0, remainder 1. The hexadecimal equivalent of 1 is 1.
Reading the remainders from bottom to top gives the hexadecimal equivalent of 7348 as 1CB4.
ii. Convert 63548 to hexadecimal:
- Divide the number by 16. 63548 ÷ 16 = 3971, remainder 12. The hexadecimal equivalent of 12 is C.
- Divide the quotient by 16. 3971 ÷ 16 = 248, remainder 3. The hexadecimal equivalent of 3 is 3.
- Divide the quotient by 16. 248 ÷ 16 = 15, remainder 8. The hexadecimal equivalent of 8 is 8.
- Divide the quotient by 16. 15 ÷ 16 = 0, remainder 15. The hexadecimal equivalent of 15 is F.
Reading the remainders from bottom to top gives the hexadecimal equivalent of 63548 as F83C.
Similar Questions
A) Research regarding how to convert (steps) Deciimal Numbers to Binary Numbers, Binary Numbers to Decimal Numbers, Binary Numbers to Hexadecimal Numbers.
The number system which uses base-16 is called hexadecimal system (or simply hex).In binary system (or base-2 number system), a total of 2 digits (0 and 1) are used to represent a number of any size (magnitude) and in octal system (or base-8 number system), a total of 8 digits (0 to 7) are used.Similarly in hexadecimal system (or base-16 number system), a total of 16 characters (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) are used to represent a number of any size (magnitude).The highest digit in hex is (F)16. The number (F)16 in binary is represented as (1111)2. Here, four binary digits (bits) are used to represent the highest hexadecimal digit.In hex to binary conversion,four bits are used to represent each hex digit.The following table shows the conversion of each hex digit into its corresponding binary digits.Hexadecimal 0 1 2 3 4 5 6 7 8 9 A B C D E FBinary 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111For example, hexadecimal number 0x5AF6 is converted into its corresponding binary form as follows:Hex Number -> 5 A F 6Binary Number -> 0101 1010 1111 0110Hence, 0x5AF6 is (0101101011110110)2Click on Live Demo to understand the conversion of a hexadecimal number into its corresponding binary form.Similarly while converting a binary number into a hex number, the binary number is first divided into groups of 4 digits each, starting from the extreme right side. Each of the four binary digits are replaced with their corresponding octal digits.If the group to the extreme left side of binary digits does not have four digits, the required number of zeros are added as a prefix to make a group of four binary digits.For example, let us try convert the following binary 1101100 number into hex.Binary Number -> 110 1100Binary Number -> 0110 1100 // After prefixing zeros in the left most groupHexadecimal Number -> 6 CHence, the hex equivalent of the given binary 1101100 is 0x6CClick on Live Demo to understand the conversion of the binary number into its corresponding hexadecimal form.Select all the correct statements from the given statements.(F3G9)16 is a hexadecimal number.Each hexadecimal digit is represented as three bit binary number.Binary number (10101110)2 is equal to the hexadecimal number (AE)16.Hexadecimal number (369)16 is equivalent of binary number (1101101001)2.
Write a C program to convert Binary to Hexadecimal number system
The number system having just these two digits – 0 and 1 – is called?A) Decimal Number SystemB) Binary Number SystemC) Octal Number SystemD) Hexadecimal Number System
What does a code converter do in digital systems? Question 7Answera.Converts decimal numbers to binary numbersb. Converts binary numbers to hexadecimal numbers c.Converts analog signals to digital signalsd.Converts one binary code to another binary code
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