How to Convert Binary to Decimal Number System
For binary numbers with n digits:
dn-1 … d3 d2 d1 d0
The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
decimal = d0×20 + d1×21 + d2×22 + …
Example
Find the decimal value of 1110012:
| binary number: | 1 | 1 | 1 | 0 | 0 | 1 |
|---|---|---|---|---|---|---|
| power of 2: | 25 | 24 | 23 | 22 | 21 | 20 |
1110012 = 1⋅25+1⋅24+1⋅23+0⋅22+0⋅21+1⋅20 = 5710
Tips for Students ▪ At first understanding the process of converting a Binary number into a Decimal Number. ▪ Then choose any Binary Number of you want to convert ▪ Now, Convert the Binary number by using the formula by yourself ▪ Then Check the Answer by using this "Binary to Decimal Converter" tool.
Binary to Decimal Conversion Table
| Binary Number | Decimal Number | Hex Number |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 10 | 2 | 2 |
| 11 | 3 | 3 |
| 100 | 4 | 4 |
| 101 | 5 | 5 |
| 110 | 6 | 6 |
| 111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | 10 | A |
| 1011 | 11 | B |
| 1100 | 12 | C |
| 1101 | 13 | D |
| 1110 | 14 | E |
| 1111 | 15 | F |
| 10000 | 16 | 10 |
| 10001 | 17 | 11 |
| 10010 | 18 | 12 |
| 10011 | 19 | 13 |
| 10100 | 20 | 14 |
| 10101 | 21 | 15 |
| 10110 | 22 | 16 |
| 10111 | 23 | 17 |
| 11000 | 24 | 18 |
| 11001 | 25 | 19 |
| 11010 | 26 | 1A |
| 11011 | 27 | 1B |
| 11100 | 28 | 1C |
| 11101 | 29 | 1D |
| 11110 | 30 | 1E |
| 11111 | 31 | 1F |
| 100000 | 32 | 20 |
| 1000000 | 64 | 40 |
| 10000000 | 128 | 80 |
| 100000000 | 256 | 100 |
Binary to Decimal Conversion Questions with Solutions
Q1. What is the binary number for decimal number 9? [UGC NET 25 Sep 2020 Shift 1]
A. 1100
B. 1001
C. 0111
D. 1011
Answer –B. 1001
Solution-
[Step 1] Divide 9 by 2 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.
[Step 2] Divide the Whole part of the Quotient from Step 1 by 2. Again, keep the Whole part and set the Remainder aside.
[Step 3] Repeat Step 2 above until the Whole part is 0.
[Step 4] Write down the Remainders in reverse order to get the answer to 9 as a binary.
Q2. What will be the decimal equivalent for the binary number 1101110?
A. 121
B. 102
C. 115
D. 110
Answer – D. 110
Solution-
▪ Given binary number = (1101110)2
▪ Calculation: (1101110)2 = (1 × 26 + 1 × 25 + 0 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 0 × 20)10
▪ (64 + 32 + 8 + 4 + 2)10 ⇒ (110)10
▪ So, the decimal equivalent of the binary number (1101110)2 is (110)10.
