Decimal to Binary Converter Calculator
Decimal to binary conversion is the process of converting a decimal number to its equivalent binary representation, consisting of 0s and 1s.
Answer
Learn about Decimal to Binary Converter
Binary is a number system that only consists of 2 digits: 0 and 1 (Unlike our normal base 10 system, which consists of 10 digits from 0 - 9.). In binary, these 'digits' are known as bits. The binary number system is used by computers to reflect the on (1) and off (0) states of a transistor. Although binary may look odd at first, reading binary numbers is straightforward. It is a positional system, so every bit is raised to the power of 2 based on its position in the number. This starts from the rightmost bit (also called the least significant bit or LSB) with the position index of 0 and goes up from there.
Decimal numbers can be converted to binary with a straightforward process. Anytime you want to keep a value within a certain set of numbers, you use the mod operator to get the remainder of a division operation between the two numbers.$$\\$$A good use case for example is to find what day of the week it'll be after an arbitrary amount of day's has passed, let's say 293. To find what day of the week it'll be, you already know that there are 7 days in a week (0 being Sunday...6 being Saturday), so we want to keep the value 293 within 7. Therefore, the operation will be 293 % 7 = 6, meaning the 293 day will fall on the 6th day of the week, which is Saturday. A similar algorithm is applied here. If we want to convert a decimal number into base 2, we have to keep it mod 2, so that it always maps to valid bits. However, we will get the integer quotient for each division operation and keep dividing it by 2, up until the quotient is equal to 0.$$\\$$For example, let's convert the decimal number 13 to binary.$$\\$$First, divide 13 by 2, with remainder.$$13/2=6+1$$13 divided by 2 is 1. We will append this 1 to our answer.$$ \begin{matrix} & & & 1 \end{matrix}$$Moving forward, we now divide the dividend from the last step by 2 again. Our dividend from last step was 6.$$6/2=3+0$$Just like last time, append 0 to our answer and then continue the process with 3 as the new dividend.$$ \begin{matrix} & & 0 & 1 \end{matrix}$$$$3/2=1+1$$Append the remainder of 1 onto the answer, and perform the last division operation on the dividend of 1.$$ \begin{matrix} & 1 & 0 & 1 \end{matrix}$$$$1/2=0+1$$Now that our dividend is 0, append the last remainder onto our answer and we have the number in binary!$$1101$$
$$\textbf{1) Problem: 23}$$$$\\$$Divide 23 by 2. The remainder becomes the end of our answer.$$23/2=11+1$$$$ \begin{matrix} & & & & 1 \end{matrix}$$Continue with the new dividend, 11.$$11/2=5+1$$$$ \begin{matrix} & & & 1 & 1 \end{matrix}$$Append the remainder and continue with the new dividend, 5.$$5/2=2+1$$$$ \begin{matrix} & & 1 & 1 & 1 \end{matrix}$$Append the remainder and continue with the new dividend, 2.$$2/2=1+0$$$$ \begin{matrix} & 0 & 1 & 1 & 1 \end{matrix}$$Finally, perform the last calculation and append the remainder. The result is 23 in binary.$$1/2=0+1$$$$ \begin{matrix} 1 & 0 & 1 & 1 & 1 \end{matrix}$$$$\textbf{Answer: 10111}$$$$\\$$$$\textbf{2) Problem: 65}$$$$\\$$Divide 65 by 2. The remainder becomes the end of our answer.$$65/2=32+1$$$$ \begin{matrix} &&&&&&1 \end{matrix}$$Continue with the new dividend, 32.$$32/2=16+0$$$$ \begin{matrix} &&&&&0&1 \end{matrix}$$Append the remainder and continue with the new dividend, 16.$$16/2=8+0$$$$ \begin{matrix} &&&&0&0&1 \end{matrix}$$Append the remainder and continue with the new dividend, 8.$$8/2=4+0$$$$ \begin{matrix} &&&0&0&0&1 \end{matrix}$$Append the remainder and continue with the new dividend, 4.$$4/2=2+0$$$$ \begin{matrix} &&0&0&0&0&1 \end{matrix}$$Append the remainder and continue with the new dividend, 2.$$2/2=1+0$$$$ \begin{matrix} &0&0&0&0&0&1 \end{matrix}$$Finally, append the remainder and continue with the new dividend, 1.$$1/2=0+1$$$$ \begin{matrix} 1&0&0&0&0&0&1 \end{matrix}$$The resulting number is 65 in binary.$$\textbf{Answer: 1000001}$$$$\\$$$$\textbf{3) Problem: 111}$$$$\\$$Divide 111 by 2. The remainder becomes the end of our answer.$$111/2=55+1$$$$ \begin{matrix} &&&&&&1 \end{matrix}$$Continue with the new dividend, 55.$$55/2=27+1$$$$ \begin{matrix} &&&&&1&1 \end{matrix}$$Append the remainder and continue with the new dividend, 27.$$27/2=13+1$$$$ \begin{matrix} &&&&1&1&1 \end{matrix}$$Append the remainder and continue with the new dividend, 13.$$13/2=6+1$$$$ \begin{matrix} &&&1&1&1&1 \end{matrix}$$Append the remainder and continue with the new dividend, 6.$$6/2=3+0$$$$ \begin{matrix} &&0&1&1&1&1 \end{matrix}$$Append the remainder and continue with the new dividend, 3.$$3/2=1+1$$$$ \begin{matrix} &1&0&1&1&1&1 \end{matrix}$$Finally, append the remainder and continue with the new dividend, 1.$$1/2=0+1$$$$ \begin{matrix} 1&1&0&1&1&1&1 \end{matrix}$$The resulting number is 111 in binary.$$\textbf{Answer: 1101111}$$$$\\$$
Watch detailed video tutorials about Decimal to Binary Converter!
How To Convert Decimal to Binary
14 minutes
Converting from decimal to binary | Applying mathematical reasoning | Pre-Algebra | Khan Academy
4 minutes
On Demand Computer Science Theory Education for Students.
© 2023 CompSciLib™, LLC. All rights reserved
info@compscilib.comContact UsCompany
About UsPricingPartnershipsImage to Text ToolAI Homework HelpCareersPrivacy PolicyTerms of Use