Math Problem Statement
1. CONVERT THE FOLLOWING DECIMAL NUMBER TO BINARY
226
Solution
To convert the decimal number 226 to binary, we need to repeatedly divide the number by 2 and record the remainders.
Let's go through the process step by step:
-
Divide 226 by 2:
with a remainder of 0. -
Divide 113 by 2:
with a remainder of 1. -
Divide 56 by 2:
with a remainder of 0. -
Divide 28 by 2:
with a remainder of 0. -
Divide 14 by 2:
with a remainder of 0. -
Divide 7 by 2:
with a remainder of 1. -
Divide 3 by 2:
with a remainder of 1. -
Divide 1 by 2:
with a remainder of 1.
Now, we read the remainders from bottom to top:
226 in decimal is equal to 11100010 in binary.
Answer: 11100010
Would you like more details on the conversion process, or have any questions? Here are some related questions for further exploration:
- What is the binary representation of 150?
- How do you convert a binary number back to decimal?
- What is the largest binary number that can be represented in 8 bits?
- How do you add two binary numbers together?
- What is the significance of binary numbers in computer systems?
Tip: Always keep track of the remainders when dividing by 2, as they determine the binary digits in reverse order.
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Math Problem Analysis
Mathematical Concepts
Number Systems
Binary Numbers
Decimal to Binary Conversion
Formulas
Divide the decimal number by 2 and record the remainders until the quotient is 0
Theorems
Division by 2 method for converting decimal to binary
Suitable Grade Level
Grades 5-7