The binary to decimal conversion questions and answers provided here will certainly assist students in better comprehending the binary to decimal number system conversion. Computers, on the other hand, only understand binary systems, but humans do not. As a result, understanding the binary to decimal conversion is essential. Many competitive examinations include questions about number system conversion. These questions can be used by students to get a rapid overview of the topics and to practice them in order to improve their understanding of the topic. You can also compare your answer to the solutions on our website.
What is Binary to Decimal Conversion?
We know that the binary to decimal number system conversion is the process of changing from a binary (base 2) to a decimal number system (base 10 number system).
To convert a binary number system to a decimal number system, follow the procedures below.
Step 1: Multiply each digit of the specified binary number by the exponents of the base starting with the rightmost digit (i.e., 20, 21, 22, and so on).
Step 2: As we move right to left, the exponents should increase by one, such that the exponents begin with 0.
Step 3: Simplify and find the sum of each of the product values obtained in the previous steps.
Binary to Decimal Conversion Questions with solutions
1. Convert 111102 into a decimal number system.
Solution:
Given binary number: 111102
111102 = (1 × 24) + (1 × 23) + (1 × 22) + (1 × 21) + (0 × 20)
111102 = (1 × 16) + (1 × 8) + (1 × 4) + (1 × 2) + (0 × 1)
111102 = 16 + 8 + 4 + 2
111102 = 3010
Thus, 3010 is the decimal equivalent of the binary number 111102.
2. Convert 01102 into a decimal system.
Solution:
Given binary number:01102
01102 = (0 × 23) + (1 × 22) + (1 × 21) + (0 × 20)
01102 = (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1)
01102 = 0 + 4 + 2 + 0
01102 = 610.
Hence, 01102 is equivalent to the decimal number system 610.
3. What is the equivalent decimal system of the binary number 11112?
Solution:
Given binary number: 11112
11112 = (1 × 23) + (1 × 22) + (1 × 21) + (1 × 20)
11112 = (1 × 8) + (1 × 4) + (1 × 2) + (1 × 1)
11112 = 8 + 4 + 2 + 1
11112 = 1510
Therefore, 1510 is the equivalent decimal system representation for the binary number 11112.
4. How to convert the binary number 11101102 into a decimal number system?
Solution:
Given binary number: 11101102
11101102 = (1 × 26) + (1 × 25) + (1 × 24) + (0 × 23) + (1 × 22) + (1 × 21) + (0 × 20)
11101102 = (1 × 64) + (1 × 32) + (1 × 16) + (0 × 8) + (1 × 4) + (1 × 2) + (0 × 1)
11101102 = 64 + 32 + 16 + 0 + 4 + 2 + 0
11101102 = 11810
Hence, the decimal representation 11810 is equivalent to the binary number 11101102
5. Convert the binary number 01010012 into a decimal system.
Solution:
Given binary number: 01010012
01010012 = (0 × 26) + (1 × 25) + (0 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20)
01010012 = (0 × 64) + (1 × 32) + (0 × 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
01010012 = 0 + 32 + 0 + 8 + 0 + 0 + 1
01010012 = 32 + 8 + 1
01010012 = 4110
Therefore, the binary number 01010012 is equivalent to the decimal representation 4110.
6. Convert 11101012 into the decimal number system.
Solution:
Given binary number: 11101012
11101012 = (1 × 26) + (1 × 25) + (1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (1 × 20)
11101012 = (1 × 64) + (1 × 32) + (1 × 16) + (0 × 8) + (1 × 4) + (0 × 2) + (1 × 1)
11101012 = 64 + 32 + 16 + 0 + 4 + 0 + 1
11101012 = 64 + 32 + 16 + 4 + 1
11101012 = 11710
Thus, the decimal equivalent of 11101012 is 11710.
7. Convert the given binary number 1000012 into a decimal number system.
Solution:
Given binary number: 1000012
1000012 = (1 × 25) + (0 × 24) + (0 × 23) + (0 × 22) + (0 × 21) + (1 × 20)
1000012 = (1 × 32) + (0 × 16) + (0 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
1000012 = 32 + 0 + 0 + 0 + 1
1000012 = 3310.
Therefore, 3310 is the equivalent decimal system representation for the number 1000012.
8. Find the equivalent decimal system for the binary number 1100110012.
Solution:
Given binary number: 1100110012
1100110012 = (1 × 28) + (1 × 27) +( 0 × 26) + (0 × 25) + (1 × 24) + (1 × 23) + (0 × 22) + (0 × 21) + (1 × 20)
1100110012 = (1 × 256) + (1 ×128) + (0 × 64) + (0 × 32) + (1 × 16) + (1 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
1100110012 = 256 + 128 + 0 + 0 + 16 + 8 + 0 + 0 + 1
1100110012 = 256 + 128 + 16 + 8 + 1
1100110012 = 40910.
Thus, 40910 is the decimal number system representation of the binary number 1100110012.
9. Determine the equivalent decimal system for the binary system 1112.
Solution:
Given binary number: 1112
1112 = (1 × 22) + (1 × 21) + (1 × 20)
1112 = (1 × 4) + (1 × 2) + (1 × 1)
1112 = 4 + 2 + 1
1112 = 710
Therefore, 1112 is equivalent to the decimal system representation 710.
10. Convert 10010100012 into the decimal number system.
Solution: 593
Given binary number: 10010100012
10010100012 = (1 × 29) + (0 × 28) + (0 × 27) +( 1 × 26) + (0 × 25) + (1 × 24) + (0 × 23) + (0 × 22) + (0 × 21) + (1 × 20)
10010100012 = (1 × 512) + (0 × 256) + (0 ×128) + (1 × 64) + (0 × 32) + (1 × 16) + (0 × 8) + (0 × 4) + (0 × 2) + (1 × 1)
10010100012 = 512 + 0 + 0 + 64 + 0 + 16 + 0 + 0 + 0 + 1
10010100012 = 512 + 64 + 16 + 1
10010100012 = 59310
Hence, the decimal representation 59310 is equivalent to the binary number 10010100012.
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Practice Questions
Answer the following binary to decimal conversion questions:
- Convert 1001000012 into the decimal number system.
- What is the equivalent decimal system representation for the binary number 11100100002.
- Find the decimal system representation for the binary number 10011111102.
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