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 , let us align the binary values and treat them as numbers in signed representation:
-
Convert to decimal:
- in binary = (positive value).
- in binary = (since it is a signed binary value with a negative sign).
-
Subtract:
. -
Convert back to binary:
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:
- How is signed binary subtraction performed using 2's complement?
- What is the difference between signed and unsigned binary numbers?
- How do you perform binary subtraction with overflow detection?
- How do you convert a negative decimal number to its signed binary equivalent?
- 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
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