binary conversion
DESCRIPTION
A step by step method in converting binary numbers to decimal and vice-versa.TRANSCRIPT
Binary
In 1854, British mathematician In 1854, British mathematician George BooleGeorge Boole published a paper published a paper
detailing a system of logic that would detailing a system of logic that would become known as become known as Boolean algebraBoolean algebra..
His logical system proved instrumental His logical system proved instrumental in the development of the binary in the development of the binary
system, particularly in its system, particularly in its implementation in electronic circuitry.implementation in electronic circuitry.
BinaryA numbering systems that only uses two A numbering systems that only uses two
digits. digits. 00 and and 11..Rather than a base ten that we are all Rather than a base ten that we are all
familiar with.familiar with. Computers use binary to store Computers use binary to store information in a digital format.information in a digital format.
Each digit ( Each digit ( 00 or or 11) represents one bit) represents one bitEight bits are equal to one byte.Eight bits are equal to one byte.
Bit
One Binary Digit abbreviation is “b”
Can be thought of as one character Either a 1 or a 0
Byte
Eight bits make up one byte Abbreviation “B” Combination of 1’s and 0’s Can be thought of as one character
11101010
kilobit
1024 bits Abbreviation “Kb”
kilobytes
Represented by KB Slang “Kilo” Is equal to 1024 bytes 210
megabytes
Represented by MB Slang “Meg” Is equal to 1,000000 bytes One million bytes 220
gigabyte
Represented by GB Slang “Gig” Equal to 1,000,000,000 Bytes One Billion bytes 230
terabyte
Represented by TB Slang “tera” Equal to 1,000,000,000,000 Bytes One Trillion bytes 240
petabyte
Represented by PB Slang “peta” Equal to 1,000,000,000,000,000
Bytes One Thousand Trillion bytes 250
exabyte
Represented by EB Slang “exa” Equal to
1,000,000,000,000,000,000 Bytes
One Million Trillion bytes 260
All printed materialin the world would use about 5 Exabytes
Think of Binary as light bulbs
that are either ON or Off
All eight of these Light bulbs would represent one byte
One Light bulb represents one One Light bulb represents one BitBit
Think of Binary as light bulbs
that are either ON or Off
11 00 00 00 00 00 00 11
Binary ExerciseBinary Exercise
Bit Postion Bit 8 Bit 7 Bit 6 Bit 5 Bit 4 Bit 3 Bit 2 Bit 1 Total Binary ValuePosition Value
if ON128 64 32 16 8 4 2 1 255
Position Valueif OFF
0 0 0 0 0 0 0 0 0
Turn a Postion ON
1 0 0 0 0 0 0 1
Here we would ADD
The Postion Value
Here we bringThe Postion
Value DOWN
128 1 129
In this incidence our binary Number 10000001 would have a value of 129Because Postion 8 is ON Postion 7 is OFF Postion 6 is OFF Position 5 is OFF Position 4 is Off
Postion 3 is OFF Postion 2 is OFF and Position 1 is ON.
Binary Exercise
Binary
Figuring Binary. Starting on the right going to the left The first digit will be 1 The second digit will be 2 The third digit will be 4 The fourth digit will be 8 The fifth digit will be 16 The sixth digit will be 32 The seventh digit will be 64 The eighth digit will be 128
Binary
Base Ten numbers are tabulated Left to Right.
Binary
Binary numbers are tabulatedRight to Left.
Example10000000The 1st – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 0 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 128
Example10000001The 1st digit would be OnThe 2nd – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 129
Example10000011The 1st digit would be OnThe 2nd digit would be OnThe 3rd – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 +128
Add the bits The value of the number would be Total 131
Example10000111The 1st- 3rd digit would be OnThe 4th – 7th digit would be OffThe Eighth digit would be On
The first digit will be 1 1 The second digit will be 2
2 The third digit will be 4 4 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64
0 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 135
Example11000000The 1st- 6th digit would be OffThe 7th digit would be OnThe 8th digit would be On
The first digit will be 1 0 The second digit will be 2
0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64
64 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 192
Think of Binary as light bulbs
that are either ON or Off
11 11 00 00 00 00 00 00
What is the What is the value?value?
192192
Example11111111The 1st- 8th digit would be On
The first digit will be 1 1 The second digit will be 2
2 The third digit will be 4
4 The fourth digit will be 8 8 The fifth digit will be 16 16 The sixth digit will be 32 32 The seventh digit will be 64
64 The eighth digit will be 128 +128
Add the bits
The value of the number would be Total 255
Think of Binary as light bulbs
that are either ON or Off
11 11 11 11 11 11 11 11
What is the What is the value?value?
255255
128128 6464 3232 1616 88 44 22 11
Using Calculatorto figureBinary Numbers
First we would open Calculator Start/All Programs/Accessories/CalculatorFrom the Calculator go to View and down To SCIENTIFIC
Scientific
This is the Scientific Calculator The next thing we would need to do
in select BIN for Binary
Next we would enter the Binary number
For example
10000000
After entering the Binary number we would then select the
Dec Radio Button
We now see the answer to the problemIs
128
Think of Binary as light bulbs
that are either ON or Off
11 11 00 00 00 00 00 00
What is the What is the value?value?
192192
ICT 1
Decimal to Binary
It follows a starightforward method. It involves dividing the number to be
converted, say N by 2 (since binary is in base 2) until we reach the division of (1/2), also making note of all remainders.
Example 1: Convert 98 from decimal to binary Divide 98 by 2, make note of all the
remainder. Continue dividingquotientsby 2,
making notes of the remainder. Also, note the star beside the last
remainder.
Division Remainder, R
98/2 = 49 R=0
49/2 = 24 R=1
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
The sequance of remainders going up gives the answer. Starting from 1*, we have 1100010.Therefore, 98 in decimals is 1100010 in binary
Example 2: Convert 21 into binary
Division Remainder, R
21/2 = 10 R=1
10/2 = 5 R=0
5/2 = 2 R=1
2/2 = 1 R=0
1/2 = 0 R=1
Therefore, 21 in decimals is 10101 in binary
Binary to decimal
Conversion follows the same steps as decimal to binary, except in reverse order.
We can begin by multiplying 0 x 2 and adding 1.
We continue to multiply the numbers in the “results” column by 2, and adding the digits from left to right in our binary numbers.
Example 1: Convert 11101 from binary to decimal
Operations Result
0 x 2 + 1 1
1 x 2 + 1 3
3 x 2 + 1 7
7 x 2 + 0 14
14 x 2 + 1 29
Therefore, 11101 in binary is 29 in decimal.