Introduction to Binary

A short introduction to the basics of binary to decimal conversion, computation, and interpretation.

Lesson 1 - Binary Basics

What is binary?

Binary is a set of 1s and 0s used to represent different numerical values, called decimals, or even different voltages or polarities: 1 for a positive or on state, and 0 for a negative or off state.

100 1011

Each binary digit is called a bit. 8 bits make a byte.

 

How is binary read?

In order to read binary, it must first be determined for what purpose the binary numbers are being used. Are they going to represent numbers? Voltages? Polarities?

Let's assume the purpose is to represent a number. In order to read the 1s and 0s, a conversion must take place. This conversion changes the binary numbers to the decimal number that is being represented.

Binary numbers can even be converted to hexadecimal numbers which then allows for a conversion to ASCII, a system that represents text. Binary can be used to create words.

Match the following terms

  • 1 bit
    A single binary number
  • 1 byte
    8 binary numbers
  • 1
    positive
  • 0
    negative

True or False

  • Binary can be used to represent words.

Lesson 2 - Binary Computation

Binary Computation - Decimal Conversion Overview

When converting a binary value to a decimal value, a simple computation takes place.

  • Binary numbers have a base of 2. This base must be used when converting from binary to decimal.
  • The binary numbers are counted, and that count helps determine the value of the superscript that is used on the base of 2 for each number.
  • The base of 2 with its appropriate superscript is multiplied by its corresponding bit, then added to the rest of the multiplied bases and bits.

Example:

binary number: 1 1 1 0 0 1
power of 2: 2^5 2^4 2^3 2^2 2^1 2^0

111001 = 1 x 2^5 + 1 x 2^4 + 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

= 57

Binary Computation - Decimal to Binary

Just like how you can convert from binary to decimal, you can also convert from decimal to binary.

 

True or False

  • You cannot convert from decimal to binary.
  • You can convert from binary to decimal.

Binary has a base of

  • 10
  • 1
  • 2
  • 0