Converting A Binary Number to Decimal and to Hexadecimal


Binary

In order to be able to convert a decimal number to binary, one must have a basic understanding of the decimal, binary and hexadecimal numbering systems. Decimal numbers are used often in mathematics, and are 10 digits (0 - 9), which occupy a decimal place. Binary numbers are 1s and 0s to us, but to computers the number one represents the high or on setting and the number zero, would mean low or off setting in a computer. Binary is used in order to represent computer data, and it can be grouped together into bytes. The binary system is able to represent information, using two mutually exclusive states, and it is a base-2 number system.

The way used, to convert the decimal number 3078 to binary code was this:

The number 3078 would have to be subtracted from either a 1 or a 0, depending on whether the number is even or odd. Then the number would be divided by 2, and the integer quotient is divided by 2 again; the steps are repeated for all the iterations. The steps are repeated until the quotient has reached zero, then the remainders of each iterations, are used to determine if the number of that iteration is a 1 or a 0, in order to find our binary number.

3078 therefore the binary number is = 0

(3078 – 0)/2 = 1539 therefore the binary number is = 1

(1539 – 1)/2 = 769 therefore the binary number is = 1

(769 - 1)/2 = 384 therefore the binary number is = 0

(384 - 0)/2 = 192 therefore the binary number is = 0

(192 - 0)/2 = 96 therefore the binary number is = 0

(96 - 0)/2 = 48 therefore the binary number is = 0

(48 - 0)/2 = 24 therefore the binary number is = 0

(24 - 0)/2 = 12 therefore the binary number is = 0

(12 - 0)/2 = 6 therefore the binary number is = 0

(6 - 0)/2 = 3 therefore the binary number is = 1

(3 - 1)/2 = 1 therefore the binary number is = 1

Therefore; 3078 in Binary is 110000000110

The hexadecimal number system uses the base of 16 system, which are very useful for representing long binary values; the hexadecimal number system can be 0-9 or A-F. It is common to find binary numbers consisting of 8, 16 and even 32 digits, when working with computers. It is not easy to work with lots of 16 or 32 binary numbers; therefore, the binary numbers have to be arranged into groups of 4 bits, to make the best use of the hex numbering system.

In order to convert the binary number 110000000110, which is 3078, to hexadecimal, the following steps were taken.

First we would need to break the binary digits into groups of four, then second using the hexadecimal conversation chart, the right numbers and letters can be assigned to the groups of four.

C 0 6

Therefore, the same number 3078 whose binary number is 110000000110, in hexadecimal it would be C06

Resources

http://www.wiley.com/legacy/college/calter/0471695939/add_mat/binaryhexa...

http://www.reelreality.com/files/Understanding_Binary-Hexadecimal.pdf

http://www.bottomupcs.com/csbu.pdf
 

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