Binary
All computer data is represented using binary, a number system that uses 0s and 1s. Binary digits can be grouped together into bytes.
Source: https://www.bbc.co.uk/bitesize/guides/zwsbwmn/revision/1
Computers use binary - the digits 0 and 1 - to store data. A binary digit, or bit, is the smallest unit of data in computing. It is represented by a 0 or a 1. Binary numbers are made up of binary digits (bits), eg the binary number 1001.
Source: https://www.bbc.co.uk/bitesize/guides/zwsbwmn/revision/1
Binary system - how to convert from base 10 (whole number) to binary number.
10 in Binary
10 in binary is 1010. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits). We have used 4 bits to represent 10 in binary. In this article, we will show how to convert the decimal number 10 to binary.
10 in Binary: 10₁₀ = 1010₂
10 in Octal: 10₁₀ = 12₈
10 in Hexadecimal: 10₁₀ = A₁₆
1010₂ in Decimal: 10₁₀
Source: https://www.cuemath.com/numbers/10-in-binary/
How to Convert 10 in Binary?
Step 1: Divide 10 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
Dividend
Remainder
10/2 = 5
0
5/2 = 2
1
2/2 = 1
0
1/2 = 0
1
Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 10.
Therefore, the binary equivalent of decimal number 10 is 1010.
Binary addition / subtraction.
The binary addition & subtraction is similar to the decimal number system. But the main difference between these two is, binary number system uses two digits like 0 & 1 whereas the decimal number system uses digits from 0 to 9 and the base of this is 10.
Source: https://www.elprocus.com/binary-addition-and-subtraction/
What is Binary Addition & Subtraction?
If a computer is accomplished in handling 5-bit numbers like -1101 where the minus is a sign bit and remaining digits are magnitude bits then this 5-bit number can be represented like 11101. Here in this digit, the first digit ‘1’ specifies the negative sign as well as remaining 4 digits are the magnitude of the numbers.
In the same way, 01101 denotes the +1101 binary numbers.
A negative (-) number is also denoted using the concept of the magnitude of the number’s 1’s complement.
Source: https://www.elprocus.com/binary-addition-and-subtraction/
Binary Addition.
Binary addition is much like your normal everyday addition (decimal addition), except that it carries on a value of 2 instead of a value of 10.
For example: in decimal addition, if you add 8 + 2 you get ten, which you write as 10; in the sum this gives a digit 0 and a carry of 1. Something similar happens in binary addition when you add 1 and 1; the result is two (as always), but since two is written as 10 in binary, we get, after summing 1 + 1 in binary, a digit 0 and a carry of 1.
Therefore in binary:
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (which is 0 carry 1)
Source: http://web.math.princeton.edu/math_alive/1/Lab1/BinAdd.html
Binary Subtraction.
Binary subtraction is one of the four binary operations, where we perform the subtraction method for two binary numbers (comprising only two digits, 0 and 1). This operation is similar to the basic arithmetic subtraction performed on decimal numbers in Maths. Hence, when we subtract 1 from 0, we need to borrow 1 from the next higher order digit, to reduce the digit by 1 and the remainder left here is also 1.
Binary Subtraction
0 – 0 = 0
1 – 0 = 1
1 – 1 = 0
0 – 1 = 1 (Borrow 1)
Source: https://byjus.com/maths/binary-subtraction/