How to Find the Binary Number of a Decimal
Most numbers used in our daily lives are notated using a decimal (or base 10) system. In the binary system, two numbers (0 and 1) are used to determine each place value. Each place value differs from an adjoining place value by a factor of two. The binary number 101 translates into two to the second power plus two to the zero power. Converting from decimal to binary requires some simple division and multiplication.
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Instructions
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Divide the decimal number by two. Write the remainder (either a 0 or 1) on a sheet of paper. For example, to find the binary form of the decimal number 450, divide 450 by two to yield a quotient of 225 with no remainder (450/2 = 225). A zero is written on the paper.
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Divide the quotient (the answer in a division equation) from the previous step by two and record the remainder next to the remainder from the previous division. Continuing the example, 225 is divided by two to yield 112 with a remainder of one (225/2 = 112 R1). The remainder one is recorded next to the zero from the previous division to give 01.
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Repeat the divisions until the dividend (the number being divided) is zero adding the remainders to the growing sequence on the paper. The rest of the divisions for the example are 112/2 = 56 R0, 56/2 = 28 R0, 28/2 = 14 R0, 14/2 = 7 R0, 7/2 = 3 R1, 3/2 = 1 R1, and 1/2 = 0 R1. Recording the remainders produces the series 010000111.
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Invert the order of the remainders from left to right. The series in the example is 010000111. Reversing their order yields 111000010. This is the binary form of the decimal number 450.
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Check the binary number by converting back to decimal form. Binary numbers are converted to decimal by adding the exponent of two for each place held by a 1, counting from left to right and beginning with two to the zero power. The binary number 111000010 then becomes 2 to the 8th power + 2 to the 7th power + 2 to the 6th power + 2 to the 1st power = 256 + 128 + 64 + 2 = 450.
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Convert decimal fractions to binary fractions by multiplying the fraction by two and recording the whole number at each step until the fractional decimal of the product is zero. The decimal fraction 0.125 is converted by 0.125 x 2 = 0.25, 0.25 x 2 = 0.50, and 0.50 x 2 = 1.00. The binary number for 0.125 is 0.001.
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