Convert Binary to Decimal and Decimal to Binary Numbers

Custom Search


Computer and New Technologies Simply Explained
Computers
Mobile Learning
Free JavaScript Tutorials
Free HTML5 Canvas Tutorials
Free Tutorials on iBooks
Use of New Technologies in Education
Glossary of Computer Technology and Internet Terms
Hardware
Internet
Security
Software
Computer Programming
Computer Graphics

Convert Binary to Decimal Numbers

A tutorial on how to convert decimal to binary and binary to decimal numbers with full explanations, exercises and answers.

The digits 0, 1, 9 are to write any number in the decimal system. Likewise, we use 0 and 1 to write numbers in the binary number system.

In decimal number system which is also called the base-10 system , the decimal number 149 is written as follows:

149 = 1*102 + 4*101 + 9*100


The binary or base-2 number 1 0 0 1 0 1 0 1 can be converted to a decimal number as follows:
1*27 + 0*26 + 0*25 + 1*24 + 0*23 + 1*22 + 0*21 + 1*20
= 128 + 16 + 4 + 1
= 149


The binary number 1 0 0 1 0 1 0 1 is written as 149 in the decimal system.

Convert Decimal Numbers to Binary

To convert a decimal number into a binary number, we carry out successive divisions by 2 and use the reminders of the successive divisions.

Example: Convert the decimal number 123 to a binary number.

123 ÷ 2 = 61 , reminder = 1 , least significant bit, goes to the right.
61 ÷ 2 = 30 , reminder = 1
30 ÷ 2 = 15 , reminder = 0
15 ÷ 2 = 7 , reminder = 1
7 ÷ 2 = 3 , reminder = 1
3 ÷ 2 = 1 , reminder = 1
1 ÷ 2 = 0 , reminder = 1 , Most significant bit, goes to the left.

The decimal number 123 in written as 1 1 1 1 0 1 1 in binary.

We can easily check by converting 1 1 1 1 0 1 1 into decimal as follows:

1*26 + 1*25 + 1*24 + 1*23 + 0*22 + 1*21 + 1*20 = 64 + 32 + 16 + 8 + 2 + 1 = 123

A Decimal to Binary Converter that may be used to convert decimal numbers to binary form.

Exercises with Answers

A - Convert the binary numbers into decimal numbers

  1. 11
  2. 101
  3. 1111
  4. 110111011
  5. 1111100011110011

B - Convert the decimal numbers into binary numbers

  1. 7
  2. 13
  3. 128
  4. 1678
  5. 12359

Answers to Above Exercises

A - Convert the binary numbers into decimal numbers

  1. 11 = 1*21 + 1*20 = 2 + 1 = 3
  2. 101 = 1*22 + 0*21 + 1*20
    = 4 + 1
    = 5
  3. 1111 = 1*23 + 1*22 + 1*21 + 1*20
    = 8 + 4 + 2 + 1
    = 15
  4. 110111011 = 1*28 + 1*27 + 0*26 + 1*25 + 1*24 + 1*23 + 0*22 + 1*21 + 1*20
    = 256 + 128 + 32 + 16 + 8 + 2 + 1
    = 443
  5. 1111100011110011 = 1*215 + 1*214 + 1*213 + 1*212 + 1*211 + 0*210 + 0*29 + 0*28 + 1*27 + 1*26 + 1*25 + 1*24 + 0*23 + 0*22 + 1*21 + 1*20
    = 32768 + 16384 + 8192 + 4096 + 2048 + 128 + 64 + 32 + 16 + 2 + 1
    = 63731

B - Convert the decimal numbers into binary numbers

    In what followr r means the reminder of the division.
  1. 7 ÷ 2 = 3 , r = 1
    3 ÷ 2 = 1 , r = 1
    1 ÷ 2 = 0 , r = 1
    Hence 7 in binary is written as 111

  2. 13 ÷ 2 = 6 , r = 1
    6 ÷ 2 = 3 , r = 0
    3 ÷ 2 = 1 , r = 1
    1 ÷ 2 = 0 , r = 1
    Hence 13 in binary is written as 1101

  3. 128 ÷ 2 = 64 , r = 0
    64 ÷ 2 = 32 , r = 0
    32 ÷ 2 = 16 , r = 0
    16 ÷ 2 = 8 , r = 0
    8 ÷ 2 = 4 , r = 0
    4 ÷ 2 = 2 , r = 0
    2 ÷ 2 = 1 , r = 0
    1 ÷ 2 = 0 , r = 1
    Hence 128 in binary is written as 10000000

  4. 1678 ÷ 2 = 839 , r = 0
    839 ÷ 2 = 419 , r = 1
    419 ÷ 2 = 209 , r = 1
    209 ÷ 2 = 104 , r = 1
    104 ÷ 2 = 52 , r = 0
    52 ÷ 2 = 26 , r = 0
    26 ÷ 2 = 13 , r = 0
    13 ÷ 2 = 6 , r = 1
    6 ÷ 2 = 3 , r = 0
    3 ÷ 2 = 1 , r = 1
    1 ÷ 2 = 0 , r = 1
    Hence 1678 in binary is written as 11010001110

  5. 12359 ÷ 2 = 6179 , r = 1
    6179 ÷ 2 = 3089 , r = 1
    3089 ÷ 2 = 1544 , r = 1
    1544 ÷ 2 = 772 , r = 0
    772 ÷ 2 = 386 , r = 0
    386 ÷ 2 = 193 , r = 0
    193 ÷ 2 = 96 , r = 1
    96 ÷ 2 = 48 , r = 0
    48 ÷ 2 = 24 , r = 0
    24 ÷ 2 = 12 , r = 0
    12 ÷ 2 = 6 , r = 0
    6 ÷ 2 = 3 , r = 0
    3 ÷ 2 = 1 , r = 1
    1 ÷ 2 = 0 , r = 1
    Hence 12359 in binary form is written as follows 11000001000111


Use of New Technologies in Education
- Computer and New Technologies Simply Explained - Computers - Mobile Learning -
Free JavaScript Tutorials -
Free HTML5 Canvas Tutorials - Free Tutorials on iBooks - Hardware - Internet -
Security - Software - Computer Programming - Computer Graphics
Glossary of Computer Technology and Internet Terms
Facebook Google Twitter


Author - e-mail

Updated: January 2015

Copyright © 2010 - 2015 - All rights reserved - A Dendane