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What is a Decimal?

In algebra, a decimal number can be defined as a number whose part and the fractional part is separated by a decimal point. The dot in a decimal number is called a . The digits following the decimal point show a value smaller than one.

Here's an example of a decimal number 17.48, in which 17 is the whole number, while 48 is the decimal part.

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Decimals are based on the preceding powers of 10 . Thus, as we move from left to right, the place value of digits gets divided by 10, meaning the decimal place value determines the tenths, hundredths and thousandths. A tenth means one tenth or 1/10. In decimal form, it is 0.1. Hundredth means 1/100. In decimal form, it is 0.01.

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What is a Binary?

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Binary is a base-2 number system invented by Gottfried Leibniz that's made up of only two numbers or digits: 0 (zero) and 1 (one). This numbering system is the basis for all binary code, which is used to write digital data such as the computer processor instructions used every day.

The 0s and 1s in binary represent OFF or ON, respectively. In a transistor, a "0" represents no flow of electricity, and "1" represents electricity being allowed to flow. In this way, numbers are represented physically inside the computing device, permitting calculation. This concept is further explained in our section on how to read binary numbers.

Why do computers use binary?

Binary is still the primary language for computers and used with electronics and computer hardware for the following reasons.

It is a simple and elegant design.

Binary's 0 and 1 method is quick to detect an electrical signal's off (false) or on (true) state.

Having only two states placed far apart in an electrical signal makes it less susceptible to electrical interference.

The positive and negative poles of magnetic media are quickly translated into binary.

Binary is the most efficient way to control logic circuits.

How to read binary numbers

The following chart illustrates the binary number 01101000. Each column represents the number two raised to an exponent, with that exponent's value increasing by one as you move through each of the eight positions. To get the total of this example, read the chart from right to left and add each column's value to the previous column: (8+32+64) = 104. As you can see, we do not count the bits with a 0 because they're "turned off."

The next example is 11111111 in binary, the maximum 8-bit value of 255. Again, reading right to left we have 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.

Steps to Convert from Decimal to Binary

If you don't have a calculator to hand, you can easily convert a decimal number to binary using the remainder method. This involves dividing the number by 2 recursively until you're left with 0, while taking note of each remainder.

1.Write down the decimal number.

2.Divide the number by 2.

3.Write the result underneath.

4.Write the remainder on the right hand side. This will be 0 or 1.

5.Divide the result of the division by 2 and again write down the remainder.

6.Continue dividing and writing down remainders until the result of the division is 0.

The most significant bit (MSB) is at the bottom of the column of remainders and the least significant bit (LSB) is at the top.

Steps to Convert Binary to Decimal

Converting from binary to decimal involves multiplying the value of each digit (i.e. 1 or 0) by the value of the placeholder in the number

1.Write down the number.

2.Starting with the LSB, multiply the digit by the value of the place holder.

3.Continue doing this until you reach the MSB.

4.Add the results together.

Test Yourself!

For each question, choose the best answer. The answer key is below.

1.What is 548 in binary?

101010

111000111

1111111111

1000100100

2.What is 11111111 in decimal?

255

254

128

256

3.Convert 10000001 to decimal

2

129

130

256

Answer Key

Question 1: 1000100100

Question 2: 255

Question 3: 129

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

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