Table of Contents
Introduction to the Binary Number System
- The binary number system is a base-2 number system that uses only the digits 0 and 1. In the binary number system, every number is represented by a sequence of 0s and 1s. For example, the number 12 can be represented as:
- The number 12 can also be represented in base 10, which is the number system we use everyday. In base 10, the number 12 is written as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. In other words, the number 12 can be written as a number that has one digit to the left of the decimal point and two digits to the right of the decimal point.
- The number 12 can also be represented in base 2, which is the binary number system. In base 2, the number 12 is written as 1, 10. In other words, the number 12 can be written as a number that has one digit to the left of the binary point and two digits to the right of the binary point.
- The number 12 can also be represented in base 16, which is the hexadecimal number system. In base 16, the number 12 is written as 1, 12. In other words, the number 12 can be written as a number that has one digit to the left of the hexadecimal point and two digits to the right of the hexadecimal point.
What is a Binary Division?
Binary division is a mathematical operation that divides one binary number by another. The result is a decimal number that represents the quotient, or the number of times the divisor can be divided into the dividend without remainder.
Rules of Binary Division
The rules of binary division are as follows:
1. To divide two binary numbers, divide the leftmost digit of the dividend by the leftmost digit of the divisor, and write the result down.
2. If the leftmost digit of the dividend is 0, ignore it and move on to the next digit.
3. If the leftmost digit of the dividend is not 0, and the leftmost digit of the divisor is not 0, subtract the two digits and write the result down.
4. Repeat steps 2 and 3 until there are no more digits to divide.
5. Write the final result down as the answer.
Four Steps to Binary Division
In binary division, the dividend is divided by the divisor using only the digits of 0 and 1. The quotient is the result of the division, and the remainder is the value left over after the division is complete.
To divide a dividend by a divisor in binary, follow these four steps:
Step 1: Write the dividend and the divisor side by side with a slash between them.
864 / 16
Step 2: Begin dividing the dividend by the divisor, using the digits of 0 and 1. The first digit in the dividend goes to the quotient, and the second digit in the dividend goes to the remainder.
8 / 1 = 8
R 0
6 / 1 = 6
R 1
Step 3: Write the quotient and the remainder below the dividend and divisor.
864 / 16
8 / 1 = 8
R 0
6 / 1 = 6
R 1
2 / 1 = 2
R 0
Step 4: Carry the remainder of the division from the previous step to the next step, and continue dividing the dividend by the divisor.
2 / 1 = 2
R 0
1 / 1 = 1
R 0
0 / 1 = 0
R 1
864 / 16
8 / 1 = 8
R 0
6 / 1 = 6
R 1
Binary Division Examples
Example 1:
What is the result of dividing 5 by 2?
The result of dividing 5 by 2 is 2.5.
Solved Example
The average of five numbers is 14. The fifth number is 16. What are the other four numbers?
The other four numbers are 8, 12, 10, and 6.
Regarding Binary Division
When dividing two binary numbers, the result is a number with a binary representation. The dividend (the number being divided) is divided by the divisor (the number doing the dividing) and the result is the quotient (the number of times the divisor goes into the dividend). The remainder is the number left over after the division is complete.
For example, if we divide 1011 (base 2) by 3 (base 2), the result is 3 with a remainder of 1. This can be represented in binary as:
1011 (base 2) / 3 (base 2) = 11 (base 2)
3 goes into 11 three times with a remainder of 1.
How to Interpret Decimal Results in Binary Division
In binary division, the dividend (the number being divided) is divided by the divisor (the number doing the dividing) and the result is the quotient (the number of times the divisor goes into the dividend). The remainder is the value left over after the division is complete.
To interpret decimal results in binary division, divide the decimal number by 2. The result is the quotient in binary. The remainder is the value left over after the division is complete.
