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Binary Division: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Binary DivisionBinary Division: Definition and ExamplesTable of ContentsBinary Division - Rules, Steps and Examples Definition of Binary Division

Binary division is a mathematical operation performed on numbers in the binary number system (base 222), which uses only the digits 000 and 111. Similar to decimal division, binary division follows a structured process, but within the constraints of the binary system. This process involves both binary multiplication and binary subtraction as part of completing division operations.

Binary division follows four key rules: when we divide 111 by 111 we get 111, when we divide 000 by 111 we get 000, and both dividing 000 by 000 and dividing 111 by 000 are meaningless operations. Understanding these fundamental operations on binary numbers is essential since many computer technologies are built on the binary number system.

Examples of Binary Division Example 1: Dividing 1110 by 111 Problem:

Divide 111021110_211102​ by 1112111_21112​

Step-by-step solution:

Step 1, Compare the divisor with parts of the dividend. Looking at the first digit of the dividend (1), we see that 111>1111 > 1111>1, so we write 000 in the quotient.

Step 2, Next, compare the divisor with the first two digits. We see that 111>11111 > 11111>11, so we write another 000 in the quotient.

Step 3, Now compare the divisor with the first three digits. We have 111=111111 = 111111=111, so we write 111 in the quotient.

Step 4, Multiply the divisor by this digit in the quotient: 111×1=111111 \times 1 = 111111×1=111. Subtract this from the current part of the dividend: 111−111=0111 - 111 = 0111−111=0.

Step 5, Bring down the next digit (000) and compare 111>0111 > 0111>0. Write 000 in the quotient.

Step 6, Our answer is 001020010_200102​, which simplifies to 10210_2102​.

Example 2: Dividing 11100 by 10 Problem:

Divide 11100211100_2111002​ by 10210_2102​

Step-by-step solution:

Step 1, Compare the first digit of the dividend (111) with the divisor (101010). Since 10>110 > 110>1, write 000 in the quotient.

Step 2, Compare the first two digits (111111) with the divisor. Since 11>1011 > 1011>10, write 111 in the quotient.

Step 3, Multiply: 1×10=101 \times 10 = 101×10=10. Subtract: 11−10=111 - 10 = 111−10=1.

Step 4, Bring down the next digit (111) to get 11. Compare with the divisor. Since 11>1011 > 1011>10, write 111 in the quotient.

Step 5, Multiply: 1×10=101 \times 10 = 101×10=10. Subtract: 11−10=111 - 10 = 111−10=1.

Step 6, Bring down the next digit (000) to get 101010. Compare with the divisor. Since 10=1010 = 1010=10, write 111 in the quotient.

Step 7, Multiply: 1×10=101 \times 10 = 101×10=10. Subtract: 10−10=010 - 10 = 010−10=0.

Step 8, Our answer is 111021110_211102​.

Example 3: Dividing 10010 by 11 Problem:

Divide 10010210010_2100102​ by 11211_2112​

Step-by-step solution:

Step 1, Compare the first digit (111) with the divisor (111111). Since 11>111 > 111>1, write 000 in the quotient.

Step 2, Compare the first two digits (101010) with the divisor. Since 11>1011 > 1011>10, write 000 in the quotient.

Step 3, Compare the first three digits (100100100) with the divisor. Since 100>11100 > 11100>11, write 111 in the quotient.

Step 4, Multiply: 1×11=111 \times 11 = 111×11=11. Subtract: 100−11=1100 - 11 = 1100−11=1. We do this by using binary subtraction:

0−1=10 - 1 = 10−1=1 (borrow 111 from the next column)

10−1=110 - 1 = 110−1=1

1−0=11 - 0 = 11−0=1

So 100−11=1100 - 11 = 1100−11=1

Step 5, Bring down the next digit (111) to get 111111. Compare with the divisor. Since 11=1111 = 1111=11, write 111 in the quotient.

Step 6, Multiply: 1×11=111 \times 11 = 111×11=11. Subtract: 11−11=011 - 11 = 011−11=0.

Step 7, Bring down the next digit (000). Since 0110 011, write 000 in the quotient and we're left with a remainder of 000.

Step 8, Our answer is 1102110_21102​.

Comments(2)DDanceTutorKurtNovember 5, 2025This binary division glossary page is great! I've used it to help my students grasp the concept. Clear examples made it easy for them to learn.

NNatureLover89September 16, 2025I’ve been helping my son with binary math, and this page on binary division was a lifesaver! The examples made it so much easier to explain—definitely bookmarking this for future lessons.

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