Monday, February 18, 2013

Binary Number System


The binary number system, or base-2 number system, signifies numeric values using two numbers, 0 and          1.The usual binary number system or base-2 system is a positional symbol with a radix of 2.


Understanding How to Convert Octal to Binary is always challenging for me but thanks to all math help websites to help me out.

For example:

102 is a binary number.

Therefore,

the first 10 numbers in binary notation 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 in decimal notation,

are 02, 12, 102, 112, 1002, 1012, 1102, 1112, 10002, and 10012.


Binary number's place value

solving decimal numbers to binary numbers:



Example 1:

Convert the number 5 to the binary number system.

Solution:

The given decimal number is 5.

We have to convert 5 into binary number system by dividing the number 2.

Divide 5 by 2 that is 5 ÷2 =1(remainder) and the quotient is 2.

Divide 2 by 2 that is 2 ÷2 =0(remainder) and the quotient is 1.


decimal to binary

Example 2:

Convert the number 9 to the binary number system.

Solution:

The given decimal number is 9.

We have to convert 9 into binary number system by dividing the number 2.

Divide 9 by 2 that is 9 ÷2 =1(remainder) and 4 (quotient).

Then divide the quotient 4 by 2 that is 4÷2=0(remainder) and 2(quotient).

Then divide the quotient 2 by 2 that is 2÷2=0(remainder) and 1(quotient)

We have to start from the remainder that is 9 = 10012.


decimal to binary

example 3:   Converts  the  binary number 10111102 into  decimal number

Solution:

=  (1 × 26) + (0 × 25) + (1 × 24) + (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20) = 64 + 0 + 16 + 8 + 4 + 2 + 0                         = 94.

hence  1011110    =  94

My forthcoming post is on Definition of even Numbers and how to apply for neet 2013 will give you more understanding about Algebra.

solving of arithematic operations on binary numbers:



Arithmetic in binary is much like arithmetic in other numeral systems. Addition, subtraction, multiplication, and           division can be performed on binary numerals.
Addition:

The simplest arithmetic operation in binary is  addition. Adding two single-digit binary numbers is relatively                     simple, using a form of carrying:

0 + 0 → 0
0 + 1 → 1
1 + 0 → 1
1 + 1 → 0, carry 1 (since 1 + 1 = 0 + 1 × 10 in binary)

For example:
two numerals are being added together: 011012 (1310) and 101112 (2310).

01101
10111
+    -------------
100000
-------------------

Subtraction:

Subtraction   works in much the same way:

0 − 0 → 0
0 − 1 → 1, borrow 1
1 − 0 → 1
1 − 1 → 0

For  example :
1010
1110
_         --------------
0100
-----------------

Division:

Binary   division is again similar to its decimal counterpart:

for  example:

the divisor is 1012, or 5 decimal, while the dividend is 110112, or 27 decimal.

The procedure is the same as that of decimal long division,  here, the divisor 1012 goes into the first three digits 1102of the dividend one time,

1
___________
1 0 1   ) 1 1 0 1 1
− 1 0 1
-----
0 1 1



Multiplication
Multification in binary is similar to its decimal counterpart.

Two numbers A and B can be multiplied by partial products:

for each digit in B, the product of that digit in A is calculated and written on a new line, shifted leftward so that its rightmost digit lines up with the digit in B that was used. The sum of all these partial products gives the final result.


For example:

the binary numbers 1011 and 1010 are multiplied as follows:



1 0 1 1   (A)
× 1 0 1 0   (B)
---------
0 0 0 0   ← Corresponds to a zero in B
+     1 0 1 1     ← Corresponds to a one in B
+   0 0 0 0
+ 1 0 1 1
---------------
= 1 1 0 1 1 1 0

Is this topic algebra problems hard for you? Watch out for my coming posts.

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