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:

16510=101001012165_{10} = 10100101_2

Since we are using 4 bytes (32 bits), we need to pad it with leading zeros:

00000000 00000000 00000000 10100101200000000 \ 00000000 \ 00000000 \ 10100101_2

Step 2: Convert to Hexadecimal

To convert binary to hexadecimal, we group the 32-bit number into 4-bit sections:

0000 0000 0000 0000 0000 0000 1010 01010000 \ 0000 \ 0000 \ 0000 \ 0000 \ 0000 \ 1010 \ 0101

Each 4-bit group is converted to hexadecimal:

0 0 0 0 0 0 A 50 \ 0 \ 0 \ 0 \ 0 \ 0 \ A \ 5

Thus, in hexadecimal, the 4-byte storage of 165 is:

000000A51600 00 00 A5_{16}


Final Answer:

Binary Representation (4 Bytes):

00000000 00000000 00000000 10100101200000000 \ 00000000 \ 00000000 \ 10100101_2

Hexadecimal Representation (4 Bytes):

00 00 00 A51600 \ 00 \ 00 \ A5_{16}

Do you want me to explain how to convert decimal to binary and hex in more detail?


Related Questions

  1. How is the negative number -165 stored in 4 bytes using two’s complement?
  2. How does endianness (big-endian vs. little-endian) affect the storage of 165?
  3. How would 165 be stored in a system using 2 bytes instead of 4?
  4. What is the binary and hexadecimal representation of 165 in an 8-bit system?
  5. 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