Math Problem Statement
The integer 165 is stored in a computer system for 4 bytes in size. Show its storage bytes in binary and in hexadecimal.
Solution
A 4-byte (32-bit) storage means the integer 165 is stored using 4 bytes (32 bits). Let's break it down in binary and hexadecimal.
Step 1: Convert 165 to Binary
The decimal number 165 can be converted to binary:
Since we are using 4 bytes (32 bits), we need to pad it with leading zeros:
Step 2: Convert to Hexadecimal
To convert binary to hexadecimal, we group the 32-bit number into 4-bit sections:
Each 4-bit group is converted to hexadecimal:
Thus, in hexadecimal, the 4-byte storage of 165 is:
Final Answer:
Binary Representation (4 Bytes):
Hexadecimal Representation (4 Bytes):
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Related Questions
- How is the negative number -165 stored in 4 bytes using two’s complement?
- How does endianness (big-endian vs. little-endian) affect the storage of 165?
- How would 165 be stored in a system using 2 bytes instead of 4?
- What is the binary and hexadecimal representation of 165 in an 8-bit system?
- How does floating-point representation differ from integer storage?
Tip: When converting decimal to binary, always divide by 2 and record the remainders from bottom to top!
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Math Problem Analysis
Mathematical Concepts
Binary Representation
Hexadecimal Representation
Number Systems
Computer Storage
Formulas
Decimal to Binary Conversion
Decimal to Hexadecimal Conversion
Theorems
Number System Conversion
Suitable Grade Level
Grades 8-10