Question

convert the following decimal numbers to equivalent binary numbers
1) 37
2) 0.125​

Answer 1

(i) 00100101 and (ii) 0000.001

Given: Two decimal numbers 37 and 0.125.

To Find: Equivalent binary numbers of decimal numbers.

Explanation:

In algebra, a decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point.

Binary Number System: According to digital electronics and mathematics, a binary number is defined as a number that is expressed in the binary system or base 2 numeral system. It describes numeric values by two separate symbols: 1 (one) and 0 (zero). The base-2 system is the positional notation with 2 as a radix.

Every digit is referred to as a bit.

Conversion of decimal to binary numbers: A decimal number has base 10 and a binary number has base 2. In decimal to binary conversion, the base of the number also changes, i.e., from base 10 to base 2. All the decimal numbers have their equivalent binary numbers.

So, the conversion of 37 into binary number would be:

(37)₁₀ = (00100101)₂

Hence, 37 in binary number is 00100101.

So, the conversion of 0.125 into binary number would be:

(0.125)₁₀ = (0000.001)₂

Hence, 0.125 in binary number is 0000.001.

∴ (i) 00100101

  (ii) 0000.001

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