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Last updated on August 19, 2025
79 in binary is written as 1001111 because the binary system uses only two digits 0 and 1 to represent numbers. This number system is used widely in computer systems. In this topic, we are going to learn about 79 binary systems.
The process of converting 79 from decimal to binary involves dividing the number 79 by 2. Here, it is getting divided by 2 because the binary number system uses only 2 digits (0 and 1). The quotient becomes the dividend in the next step, and the process continues until the quotient becomes 0.
This is a commonly used method to convert 79 to binary. In the last step, the remainder is noted down bottom side up and that becomes the converted value. For example, the remainders noted down after dividing 79 by 2 until getting 0 as the quotient is 1001111. Remember, the remainders here have been written upside down.
In the table shown below, the first column shows the binary digits (1 and 0) as 1001111. The second column represents the place values of each digit, and the third column is the value calculation, where the binary digits are multiplied by their corresponding place values.
The results of the third column can be added to cross-check if 1001111 in binary is indeed 79 in the decimal number system.
79 can be converted easily from decimal to binary. The methods mentioned below will help us convert the number. Let’s see how it is done.
Expansion Method: Let us see the step-by-step process of converting 79 using the expansion method.
Step 1 - Figure out the place values: In the binary system, each place value is a power of 2. Therefore, in the first step, we will ascertain the powers of 2.
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
Since 128 is greater than 79, we stop at 26 = 64.
Step 2 - Identify the largest power of 2: In the previous step, we stopped at 26 = 64. This is because in this step, we have to identify the largest power of 2, which is less than or equal to the given number, 79. Since 26 is the number we are looking for, write 1 in the 26 place. Now the value of 26, which is 64, is subtracted from 79. 79 - 64 = 15.
Step 3 - Identify the next largest power of 2: In this step, we need to find the largest power of 2 that fits into the result of the previous step, 15. So, the next largest power of 2 is 23, which is less than or equal to 15. Now, we have to write 1 in the 23 places. And then subtract 8 from 15. 15 - 8 = 7.
Step 4 - Identify the next largest power of 2: Now, the largest power of 2 that fits into 7 is 22. Write 1 in the 22 places. And then subtract 4 from 7. 7 - 4 = 3.
Step 5 - Identify the next largest power of 2: Now, the largest power of 2 that fits into 3 is 21. Write 1 in the 21 places. And then subtract 2 from 3. 3 - 2 = 1.
Step 6 - Identify the next largest power of 2: Now, the largest power of 2 that fits into 1 is 20. Write 1 in the 20 places. And then subtract 1 from 1. 1 - 1 = 0. We need to stop the process here since the remainder is 0.
Step 7 - Write the values: We now write the numbers to represent 79 in binary. 1 in the 26 place 0 in the 25 place 0 in the 24 place 1 in the 23 place 1 in the 22 place 1 in the 21 place 1 in the 20 place Therefore, 1001111 is 79 in binary.
Grouping Method: In this method, we divide the number 79 by 2. Let us see the step-by-step conversion.
Step 1 - Divide the given number 79 by 2. 79 / 2 = 39. Here, 39 is the quotient, and 1 is the remainder.
Step 2 - Divide the previous quotient (39) by 2. 39 / 2 = 19. Here, the quotient is 19 and the remainder is 1.
Step 3 - Repeat the previous step. 19 / 2 = 9. Now, the quotient is 9, and 1 is the remainder.
Step 4 - Repeat the previous step. 9 / 2 = 4. Here, the quotient is 4, and 1 is the remainder.
Step 5 - Repeat the previous step. 4 / 2 = 2. Here, the quotient is 2, and 0 is the remainder.
Step 6 - Repeat the previous step. 2 / 2 = 1. Here, the quotient is 1, and 0 is the remainder.
Step 7 - Repeat the previous step. 1 / 2 = 0. Here, the remainder is 1. And we stop the division here because the quotient is 0.
Step 8 - Write down the remainders from bottom to top. Therefore, 79 (decimal) = 1001111 (binary).
There are certain rules to follow when converting any number to binary. Some of them are mentioned below:
This is one of the most commonly used rules to convert any number to binary. The place value method is the same as the expansion method, where we need to find the largest power of 2. Let’s see a brief step-by-step explanation to understand the first rule. Find the largest power of 2 less than or equal to 79. Since the answer is 26, write 1 next to this power of 2. Subtract the value (64) from 79. So, 79 - 64 = 15. Find the largest power of 2 less than or equal to 15. The answer is 23. So, write 1 next to this power. Now, 15 - 8 = 7. Find the largest power of 2 less than or equal to 7. The answer is 22. So, write 1 next to this power. Now, 7 - 4 = 3. Find the largest power of 2 less than or equal to 3. The answer is 21. So, write 1 next to this power. Now, 3 - 2 = 1. Find the largest power of 2 less than or equal to 1. The answer is 20. So, write 1 next to this power. Now, 1 - 1 = 0. Since there is no remainder, we can write 0 next to the remaining powers (25 and 24). Final conversion will be 1001111.
The division by 2 method is the same as the grouping method. A brief step-by-step explanation is given below for better understanding. First, 79 is divided by 2 to get 39 as the quotient and 1 as the remainder. Now, 39 is divided by 2. Here, we will get 19 as the quotient and 1 as the remainder. Dividing 19 by 2, we get 9 as the quotient and 1 as the remainder. Divide 9 by 2 to get 4 as the quotient and 1 as the remainder. Divide 4 by 2 to get 2 as the quotient and 0 as the remainder. Divide 2 by 2 to get 1 as the quotient and 0 as the remainder. Divide 1 by 2 to get 0 as the quotient and 1 as the remainder. We stop the division once the quotient becomes 0. Now, we write the remainders upside down to get the binary equivalent of 79, 1001111.
This rule also involves breaking of the number into powers of 2. Identify the powers of 2 and write it down in decreasing order i.e., 26, 25, 24, 23, 22, 21, and 20. Find the largest power that fits into 79. Repeat the process and allocate 1s and 0s to the suitable powers of 2. Combine the digits (0 and 1) to get the binary result.
The limitation of the binary system is that only 0s and 1s can be used to represent numbers. The system doesn’t use any other digits other than 0 and 1. This is a base 2 number system, where the binary places represent powers of 2. So, every digit is either a 0 or a 1. To convert 79, we use 0s for 25 and 24 and 1s for 26, 23, 22, 21, and 20.
Learning a few tips and tricks is a great way to solve any mathematical problems easily. Let us take a look at some tips and tricks for binary numbers up to 79.
Here, let us take a look at some of the most commonly made mistakes while converting numbers to binary.
Convert 79 from decimal to binary using the place value method.
1001111
26 is the largest power of 2, which is less than or equal to 79. So place 1 next to 26.
Subtracting 64 from 79, we get 15.
So the next largest power would be 23.
So place another 1 next to 23.
Now, subtracting 8 from 15, we get 7.
The next power is 22.
Place 1 next to 22.
Subtract 4 from 7, we get 3.
The next power is 21.
Place 1 next to 21.
Subtract 2 from 3, we get 1.
The next power is 20.
Place 1 next to 20.
Now, we just place 0s in the remaining powers of 2, which are 25 and 24.
By using this method, we can find the binary form of 79.
Convert 79 from decimal to binary using the division by 2 method.
1001111
Divide 79 by 2. In the next step, the quotient becomes the new dividend.
Continue the process until the quotient becomes 0.
Now, write the remainders upside down to get the final result.
Convert 79 to binary using the representation method.
1001111
Break the number 79 into powers of 2 and find the largest powers of 2.
We get 26. So 1 is placed next to 26. Next, 79 - 64 = 15.
Now, the largest power of 2 is 23.
Once again, 1 is placed next to 23.
Now, 15 - 8 = 7.
The next power is 22.
Place 1 next to 22.
Subtract 4 from 7, we get 3.
The next power is 21.
Place 1 next to 21.
Subtract 2 from 3, we get 1.
The next power is 20.
Place 1 next to 20.
After getting 0, fill in with zeros for unused powers of 2.
By following this method, we get the binary value of 79 as 1001111.
How is 79 written in decimal, octal, and binary form?
Decimal form - 79 Octal - 117 Binary - 1001111
The decimal system is also called the base 10 system.
In this system, 79 is written as 79 only.
We have already seen how 79 is written as 1001111 in binary.
So, let us focus on the octal system, which is base 8.
To convert 79 to octal, we need to divide 79 by 8. So 79 / 8 = 9 with 7 as the remainder.
In the next step, divide the quotient from the previous step (9) by 8.
So 9 / 8 = 1 with 1 as the remainder.
The division process stops here because the quotient is now 0.
Here, 7 and 1 are the remainders, and they have to be written in reverse order.
So, 117 is the octal equivalent of 79.
Express 79 - 5 in binary.
100100
79 - 5 = 74 So, we need to write 74 in binary.
Start by dividing 74 by 2.
We get 37 as the quotient and 0 as the remainder.
Next, divide 37 by 2.
Now we get 18 as the quotient and 1 as the remainder.
Divide 18 by 2 to get 9 as the quotient and 0 as the remainder.
Divide 9 by 2 to get 4 as the quotient and 1 as the remainder.
Divide 4 by 2 to get 2 as the quotient and 0 as the remainder.
Divide 2 by 2 to get 1 as the quotient and 0 as the remainder.
Divide 1 by 2 to get 0 as the quotient and 1 as the remainder.
Now write the remainders from bottom to top to get 100100 (binary of 74).
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.