Which of the following is the binary equivalent of the decimal number 35 ?
100011
Decimal to Binary Conversion Explained
The question asks for the binary equivalent of the decimal number 35. Converting a decimal number to its binary form is a fundamental concept in computer science and digital electronics. Binary numbers use a base-2 system, meaning they only use the digits 0 and 1, whereas decimal numbers use a base-10 system with digits 0 through 9.
How to Convert Decimal to Binary?
A common method for converting a decimal number to its binary equivalent is the division method. This involves repeatedly dividing the decimal number by 2 and recording the remainder at each step. The binary equivalent is then obtained by reading the remainders from bottom to top.
Step-by-Step Conversion of 35 to Binary
Let's apply the division method to convert the decimal number 35 to binary.
| Division | Quotient | Remainder |
|---|---|---|
| $35 \div 2$ | $17$ | $1$ |
| $17 \div 2$ | $8$ | $1$ |
| $8 \div 2$ | $4$ | $0$ |
| $4 \div 2$ | $2$ | $0$ |
| $2 \div 2$ | $1$ | $0$ |
| $1 \div 2$ | $0$ | $1$ |
To get the binary equivalent, read the remainders from the last one obtained (bottom) to the first one (top). The remainders in order from bottom to top are 1, 0, 0, 0, 1, 1.
Therefore, the binary equivalent of the decimal number 35 is $\text{100011}_2$.
Revision Table: Decimal and Binary Equivalents
Here is a table showing the binary equivalents for a few decimal numbers:
| Decimal Number | Binary Equivalent |
|---|---|
| $0$ | $0_2$ |
| $1$ | $1_2$ |
| $2$ | $10_2$ |
| $3$ | $11_2$ |
| $4$ | $100_2$ |
| $10$ | $1010_2$ |
| $35$ | $100011_2$ |
Additional Information: Number Systems Basics
Number systems are ways of representing numbers. The two most common systems are decimal and binary.
- Decimal System (Base-10): Uses digits 0-9. Each position in a decimal number represents a power of 10. For example, $35 = 3 \times 10^1 + 5 \times 10^0$.
- Binary System (Base-2): Uses digits 0 and 1. Each position in a binary number represents a power of 2. For example, the binary number $\text{100011}_2$ can be converted back to decimal as follows:
- $1 \times 2^5 = 1 \times 32 = 32$
- $0 \times 2^4 = 0 \times 16 = 0$
- $0 \times 2^3 = 0 \times 8 = 0$
- $0 \times 2^2 = 0 \times 4 = 0$
- $1 \times 2^1 = 1 \times 2 = 2$
- $1 \times 2^0 = 1 \times 1 = 1$
Understanding decimal to binary conversion is essential for studying digital systems, computer architecture, and low-level programming.
Important Questions from Binary Number System
Convert decimal number 26.85 into binary equivalent.
Given below are two statements
Statement I: The base of the binary number system is 2.
Statement II: Binary addition is just like decimal addition except that the rules are much simpler.
In light of the above statements, choose the correct answer from the options given below
A-F system is used in which of the following number systems?
How many unique combinations of 0's and 1's can be made with a 5-binary-digit code?
Which of the following number systems uses two numbers to represent data in computer ?
