An Introduction to Binary Subtraction
Another basic concept of binary operations in binary subtraction. We all know that the first thing we would learn in Mathematics is addition, subtraction, multiplication, and division. In binary subtraction, you will have only two elements: 0 and 1. In this topic, you will learn about binary subtraction in-depth that includes definition, the method, and binary subtraction examples.
What is Binary Subtraction?
Do you think that binary numbers can be subtracted? Yes, the subtraction of binary numbers is possible. It is very similar to the subtraction of base 10 numbers. If you add 1 + 1 + 1 the end result is 3. But according to a binary number system, the value of 1 + 1 + 1 is going to be 1 1. Here, you have to be careful while subtracting or adding because it might get a little confusing.
Binary Subtraction Rules
To make the understanding of binary numbers easier, here are a few binary subtraction rules you should remember and apply them accordingly:
1 - 1 = 0
1 - 0 = 1
0 - 1 = 1 ( you can borrow 1 from the next number)
0 - 0 = 0
Example of Subtraction of Binary Numbers
1. Subtract 1 10 from 1 1 1 0
Solution:
1 1 1 0
1 1 0 (-)
_________
1 0 0 0
_________
Now, let’s learn how to subtract binary numbers.
How do you Subtract Binary Numbers?
Let’s take the same example as the one we used above.
1 1 1 0
1 1 0 (-)
_________
1 0 0 0
_________
Step 1: You subtract the numbers in the one’s column and not down the result. In this case, the value of 0 - 1 = 0. We borrow 1 from the number in the ten’s place and continue with the subtraction.
1 1 1 0
1 1 0 (-)
_________
0
_________
Step 2: Now you subtract the values in the 10’s place. Apply the aforementioned binary subtraction rules.
1 1 1 0
1 1 0 (-)
_________
0 0
_________
Step 3: Subtract the value that is present in the hundreds place value.
1 1 1 0
1 1 0 (-)
_________
0 0 0
_________
Step 4: Since we don’t have anything in the thousand’s place, we retain it as it is.
1 1 1 0
1 1 0 (-)
_________
1 0 0 0
_________
To cross-check if the final result is correct, you need to know the decimal values of the given numbers.
Therefore,
1 1 1 0 - 1 1 0 = 1 0 0 0
14 - 6 = 8
Hence, proved.
Binary Subtraction Example
Example 1: 1 0 1 1 0 1 0 - 0 0 1 0 1 0
1 0 1 1 0 1 0
0 0 1 0 1 0 (-)
____________
1 0 1 0 0 0 0
____________
Cross-checking using the decimal equivalent of the above decimal numbers:
1 0 1 1 0 1 0 = 90
0 0 1 0 1 0 = 10
1 0 1 0 0 0 0 = 80
Subtraction using 1’s Complement
When you’re subtracting a number from another number using one’s complement, you should remember that 0 is the positive sign and 1 is the negative sign.
Binary Subtraction Rules by 1’s Complement
Step 1: First note down the 1’s complement of the number that has to be subtracted (subtrahend)
Step 2: Add Step 1’s result with the minuend.
Step 3: In case a carryover exists, you should add it to the least significant bit.
Step 4: If no carryover exists, take the one’s complement of the result.
Binary Subtraction Examples using 1’s Complement
Example 1: (1110)₂ - (11)₂
Step 1: 1’s complement of the subtrahend
1 1 1 1
0 0 1 1 (-)
_________
1 1 0 0
_________
Step 2: Adding 1’s complement of subtrahend to minuend
1 1 1 0
1 1 0 0 (+)
_________
1 1 0 1 0
_________
Step 3: Since carry over exists, shifting it to the least significant bit.
1 1 1 0
1 (+)
_________
1 0 1 1
_________
Therefore, the answer is 1 0 1 1.
FAQs on Binary Subtraction
1. What is binary subtraction?
One of the four binary operations is binary subtraction, which involves subtracting two binary values (comprising only two digits, 0 and 1). This procedure is identical to the basic arithmetic subtraction on decimal numbers that are performed in Math. As a result, when subtracting 1 from 0, we must borrow 1 from the next higher order digit in order to reduce the digit by 1, and the remainder is also 1. When subtracting fractional binary values, the same rule applies, and the decimal should be placed correctly. Kindly head over to Vedantu to know more.
2. What is a binary number?
A binary number is a number stated in the base-2 numeral system, often known as the binary numeral system, which utilises only two symbols: "0" (zero) and "1" (one) (one).
The base-2 number system is a two-radix positional notation. A bit, or binary digit, is the name given to each digit. Because of its ease of implementation in digital electrical circuitry utilising logic gates, the binary system is employed by practically all current computers and computer-based devices as a preferred form of communication over a variety of other human communication systems.
3. How to convert decimal to binary before subtracting?
The way to convert decimal to binary before subtracting is:
The number is split by two to convert from a base-10 integer to its base-2 (binary) equivalent. The rest is the least important part. The remainder of the quotient is divided by two and becomes the next least significant bit. This method is repeated until the quotient reaches one. Because each remainder must be either zero or one when dividing by two, the binary value is formed by the sequence of remainders (including the final quotient of one). For instance, (357)10 can be written as (101100101)2.
Pingala, an Indian scholar, devised a binary system for describing prosody. It was similar to Morse code since he employed binary integers in the form of short and lengthy syllables. The laghu and guru syllables were their names.
The Hindu book Chandastra by Pingala explains the building of a matrix to give each metre a distinct value. In Sanskrit, "Chandastra" literally means "knowledge of metres." The binary representations of Pingala's system increase to the right, not to the left, as in modern positional notation's binary numbers. The numbers in Pingala's system begin with one rather than zero.
5. What is a binary number system?
A binary number is described as a number that is stated in the binary system or base 2 numeral system, according to digital technology and mathematics. It uses two distinct symbols to represent numerical values: 1 (one) and 0 (zero) (zero). The positional notation with 2 as a radix is known as the base-2 system.
Due to its direct application in electronic circuits utilising logic gates, the binary system is used internally by practically all modern computers and computer-based devices. A bit is a unit of measurement for each digit. Kindly visit the Vedantu app and website for free study materials.
The rules for binary subtraction are listed below:
1 - 1 = 0
1 - 0 = 1
0 - 1 = 1 ( you can borrow 1 from the next number)
0 - 0 = 0
Here is an example of subtraction of binary numbers -
Question: Subtract 1 1 0 from 1 1 1 0
Solution: 1 1 1 0
(-) 1 1 0
__________
1 0 0 0
__________
7. How to apply 1’s Complement to binary subtraction?
Applying 1’s Complement to binary subtraction-
Step 1: The 1’s complement of the number that has to be subtracted (subtrahend) has to be noted down first.
Step 2: Step 1’s result is added with the minuend.
Step 3: You should add it to the least significant bit in case a carryover exists.
Step 4: Take the one’s complement of the result if no carryover exists.
8. How to subtract two binary numbers?
The steps for subtracting two binary numbers are:
Step 1: The numbers in one’s column are subtracted and the result is noted down. In this case, the value of 0 - 1 = 0. We borrow 1 from the number in the ten’s place and continue with the subtraction.
Step 2: Now the values in the 10’s place are subtracted. The aforementioned binary subtraction rules are applied.
Step 3: The value that is present in the hundreds place value is then subtracted.
Step 4: Since we don’t have anything in the thousand’s place, it is retained it as it is.
