when we say that binary system is also called base-2 system, what do we mean by that "base-2"?

Question

similarly decimal numeral system is also "base-10" system. what is it? i need the answers urgently as i am doing a maths project.

Answer 1

Binary:
base 2 = only two (2) digits
1 and 0

Decimal:
base 10 = only ten (10) digits
1,2,3,4,5,6,7,8,9,0

The base describes how all other numbers are formed, and defines how you create the numerals of any given set.

That is, you only use the base numbers to create the numbers from that set.

Good luck!

Answer 2

The binary system base 2 is used mainly in digital electronics and computer systems to represent 1 or 0. For example using the standard base system base ten, the number 100 in base ten is 10^2 or (10x10) but in the binary system the base is 2, so the number 100 base 10 in binary is
1 0 0
2^2 2^0 2^0
0100 0010 0000 = 010000000000 in binary.
From right to left the powers of 2 go up in increments of 1
2^0 = 1, 2^1 = 2, 2^2 = 4, 2^3 = 8,
Any time you have a base ten number it can be represented in base two by following the above example.
Ex. 246 in binary =

2 4 6
2^1 2^2 2^2 +_2^1
0010 0100 0110
binary = 001001000110 this is how your computer interprets the number 246.

Answer 3

A base-2 system expresses numbers using 2 digits, 0 and 1.
A base-10 systems uses 10 digits, 0 through 9.

People use their ten fingers to express numbers, holding up three fingers for "3" or ten fingers for "10", etc. Opening and closing both fists twice meant "20".
That's how the base-10 system was created. Digit comes from the Latin word for finger!

A three-digit number is written with
     a digit in the ones column
     a digit in the tens column, and
     a digit in the hundreds column.
Notice any pattern in the names of these columns?
     one = 10⁰
     ten = 10¹
     hundred = 10²
The columns are named after powers of 10. You can probably guess that the next column is 10³, or the "thousands" column.

It works the same way in a base-2 system.
The first column is 2⁰, or the "ones"
The next column is 2¹, or the "twos" column.
The next column is 2², or the "fours" column.
The next column is 2³, or the "eights" column
etc.

Answer 4

Base 2 only has two digits, 0 and 1. So you would count like this:
0, 1, 10, 11, 100, 101, 110, 111, 1000 etc....

You will notice that each place represents 2 raised to a power so 2^1 = 10, 2^2 = 100 and so on.

Answer 5

Base 2 means using only 2 symbols to represent any number.
Base 10 means using only 10 symbols to represent any number. For example you can represent any decimal numbers with the following 10 symbols: 0,1,2,3,4,5,6,7,8,9. To write one hundred and seven in decimal you would use 1, 0 and 7 to make 107. Similarly, you can represent any binary number with the following 2 symbols: 0,1. To write one hundred and seven in binary you would use 0 and 1 to make 1101011.

Answer 6

In base ten , the number 572 means
100___10___1
_5_____7___2

The headings are 10^0 = 1 , 10 , 100 etc

In base two, the headings are 2^0 = 1 , 2 ,4 etc

16___8___4___1
1____1___1___0

In above, 1110 base 2 = 28 base ten

Entries in base two are 1 or 0

Answer 7

the only digits in base 2 are 0 and 1, when you add you carry "2" s and subtracting you borrow "2"s

in base 10, digits are 0,1,2,3,4,5,6,7,8,9 and you carry tens and borrow tens

base 4: digits used are 0,1,2,3

etc