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Conversion Between Decimal and Binary

Posted in C Programming, C++ Programming, Computer Science, Digital Circuit, General Topics

1. How to Convert Decimal to Binary?

In computers, all data is ultimately represented using binary numbers. We need convert Decimal to Binary.

1.1 Conversion steps:

  1. Divide the number by 2.
  2. Get the integer quotient for the next iteration.
  3. Get the remainder for the binary digit.
  4. Repeat the steps until the quotient is equal to 0.

We can now explain how decimal numbers are converted to binary by giving an example.

In binary, 65 is represented as 1000001. Unlike using decimal digits 0 to 9 to represent numbers, in the binary system we only use two digits, 0 and 1 . We use 7 bits to represent 65 in binary.

In this chapter, we will show how to convert the decimal number 65 to binary.

  • 65 in Binary:65₁₀ = 1000001
  • 65 in Octal:65₁₀ = 101
  • 65 in Hexadecimal:>65₁₀ = 41₁₆
  • 1000001₂  in Decimal:6₁₀

Here are the steps to convert the decimal number 65 to binary:

  1. Divide 65 by 2, the quotient is 32 and the remainder is 1.
  2. Divide 32 by 2, the quotient is 16 and the remainder is 0.
  3. Divide 16 by 2, the quotient is 8 and the remainder is 0.
  4. Divide 8 by 2, the quotient is 4 and the remainder is 0.
  5. Divide 4 by 2, the quotient is 2 and the remainder is 0.
  6. Divide 2 by 2, the quotient is 1 and the remainder is 0.
  7. Divide 1 by 2, the quotient is 0 and the remainder is 1.

Reading the remainders in reverse order gives the binary representation of 65: 1000001.

Related:   Memory and Variables in C Programming

Therefore, the decimal number 65 is converted to the binary number 1000001.

 

1.2 Decimal to Binary Conversion Table

Decimal
Number
Binary
Number
Hex
Number
0 0 0
1 1 1
2 10 2
3 11 3
4 100 4
5 101 5
6 110 6
7 111 7
8 1000 8
9 1001 9
10 1010 A
11 1011 B
12 1100 C
13 1101 D
14 1110 E
15 1111 F
16 10000 10
17 10001 11
18 10010 12
19 10011 13
20 10100 14
21 10101 15
22 10110 16
23 10111 17
24 11000 18
25 11001 19
26 11010 1A
27 11011 1B
28 11100 1C
29 11101 1D
30 11110 1E
31 11111 1F
32 100000 20
64 1000000 40
128 10000000 80
256 100000000 100

2. How to Convert Binary to Decimal

2.1 Conversion steps:

Here are the steps to convert the binary number 100001 to decimal:

  1. Write down the binary number: 100001
  2. Assign each digit in the binary number a place value, starting from the rightmost digit with a value of 1, and doubling the value for each digit moving left:

1         0   0   0   0   0  1

64     32  16  8   4   2   1

  1. Multiply each digit in the binary number with its corresponding place value:

1 x 64 = 64

                     0 x 32 = 0

0 x 16 = 0

0 x 8 = 0

0 x 4 = 0

0 x 2 = 0

1 x 1 = 1

  1. Add up the products obtained in step 3 to obtain the decimal equivalent:

64 + 0 + 0 + 0 + 0 + 0 + 1 = 65

Therefore, the binary number 100001 is equivalent to the decimal number 33. Note that this result is different from the decimal value of 65, which was obtained earlier because of a mistake in the conversion process. The correct binary representation of the decimal number 65 is 1000001.

Related:   How to Convert Binary to Hexadecimal?

2.2 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

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