Math Problem Statement

Calculate (give answers as binary numbers without leading zeros and do not leave empty answers): a) 10100 + 1000 = ___ b) 10100 - 1000 = ___ c) 10100 x 1000 = ___

Solution

Let's break down the binary calculations from the image.

The problem involves binary numbers and basic operations (addition, subtraction, multiplication). Let's proceed with each step:

a) 10100+100010100 + 1000

The binary numbers in question are:

  • 10100210100_2 (which is 20 in decimal)
  • 100021000_2 (which is 8 in decimal)

Adding these two: 101002+10002=11100210100_2 + 1000_2 = 11100_2 Thus, the result in binary is: 11100.

b) 10100100010100 - 1000

Subtracting the same binary numbers: 10100210002=11100210002=01100210100_2 - 1000_2 = 11100_2 - 1000_2 = 01100_2 So, the result in binary is: 1100.

c) 10100×100010100 \times 1000

Multiplying the binary numbers: 101002×10002=10100000210100_2 \times 1000_2 = 10100000_2 So, the result in binary is: 10100000.

Would you like more details on the steps for each operation? Let me know if you have any further questions!

Related questions:

  1. How do you convert a binary number to decimal?
  2. What are the rules for binary addition and subtraction?
  3. How is binary multiplication different from decimal multiplication?
  4. How do you represent large numbers in binary?
  5. Can binary numbers be used in real-world applications, and how?

Tip: To check if binary addition is correct, convert the result to decimal and verify the sum.

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Math Problem Analysis

Mathematical Concepts

Binary Arithmetic
Binary Addition
Binary Subtraction
Binary Multiplication

Formulas

Binary addition: a + b
Binary subtraction: a - b
Binary multiplication: a * b

Theorems

Binary operations are based on place value in base-2 system

Suitable Grade Level

Grades 7-9