Math Problem Statement

Subtract the following binary number from the other (just type in the binary value as stored in a computer byte without the subscript; don't forget the sign digit if it applies in a byte, if the binary value is positive then you can leave out the leading zeroes in your answer):

1110 - 10011

Solution

To solve 1110100111110 - 10011, let us align the binary values and treat them as numbers in signed representation:

  1. Convert to decimal:

    • 11101110 in binary = 1414 (positive value).
    • 1001110011 in binary = 13-13 (since it is a signed binary value with a negative sign).
  2. Subtract:
    14(13)=14+13=2714 - (-13) = 14 + 13 = 27.

  3. Convert 2727 back to binary:
    2727 in binary = 11011.

Thus, the result in a computer byte (using only necessary bits) is:

11011

Let me know if you'd like step-by-step details or have further questions!


Related Questions:

  1. How is signed binary subtraction performed using 2's complement?
  2. What is the difference between signed and unsigned binary numbers?
  3. How do you perform binary subtraction with overflow detection?
  4. How do you convert a negative decimal number to its signed binary equivalent?
  5. What is 2's complement representation, and why is it used in computers?

Tip: Remember, signed binary numbers often use 2's complement to represent negative values.

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Math Problem Analysis

Mathematical Concepts

Binary Arithmetic
Signed Binary Numbers
Two's Complement

Formulas

Binary subtraction using two's complement
Conversion between decimal and binary representations

Theorems

Two's Complement Theorem for Signed Binary Numbers

Suitable Grade Level

Grades 9-12