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Binary Number System

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In a binary number (or base two) system, we use only two digits: 0 and 1.

The following diagrams show the place values for binary numbers and how to convert from binary to decimal.

Binary to Decimal

Convert From Binary To Decimal

Like base ten numbers, we can determine the value of a base two number by placing each digit in its respective place value, then writing its expanded notation.

Example:
Find the value of each of the following binary numbers, giving the values in decimal numbers:
a)1012
b)10112
c)101012

Solution:
a)

24 23 22 21 20
1 0 1

1012 = 1 × 22 + 0 × 21 + 1 × 20
= 4 + 0 + 1
= 510

b)
24 23 22 21 20
1 0 1 1

10112 = 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20
= 8 + 0 + 2 + 1
= 1110

c)
24 23 22 21 20
1 0 1 0 1

01012 = 1 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20
= 16 + 0 + 4 + 0 + 1
= 2110

How To Convert Binary To Decimal?



Convert From Decimal To Binary

We can convert a decimal number into a binary number by repeatedly dividing the base ten number by two. Then, write the remainders from the bottom to the top as the answer:

Example:
Write each of the following base ten numbers as a binary number:
a)510
b)7810

Solution:

a)

510 = 1012


b)
Convert Decimal to Binary
7810 = 10011102

Base 10 to Base 2 (Decimal to Binary) Conversion
A demonstration of the repeated divide by 2 method for converting numbers from base 10 (or decimal) into base 2 (or binary) form.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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