# Binary Calculator

Binary system is actually a numerical system which uses only 2 symbols, 0 and 1. Because of its simple implementation in Electronic digital circuitry making use of logic gates, all contemporary computers make use of the binary system internally.

Listed below are some standard conversions among binary values and decimal values.

to base

Refrence

decimal 0 = 0 in binary
decimal 1 = 1 in binary
decimal 2 = 10 in binary
decimal 3 = 2 + 1 = 11 in binary
decimal 4 = 22 = 100 in binary
decimal 7 = 22 + 2 + 1 = 111 in binary
decimal 8 = 23 = 1000 in binary
decimal 10 = 23 + 2 = 1010 in binary
decimal 16 = 24 = 10000 in binary
decimal 20 = 24 + 22 = 10100 in binary

## Binary Addition Calculator

The adding of binaries is comparable to the decimal system. The sole difference would be to carry over whenever the result is 2.

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, carry 1 = 10

For example:
0 1 1 0 1
+ 1 0 1 1 1
---------------------
= 1 0 0 1 0 0

## Binary Subtraction Calculator

Subtraction works similarly:
0 - 0 = 0
0 - 1 = 1, borrow 1 = -1
1 - 0 = 1
1 - 1 = 0

For example:
1 0 1 1 1
+ 0 1 1 0 1
---------------------
= 0 1 0 1 0