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Understanding Binary Addition and Subtraction
Jul 16, 2024
Binary Addition and Subtraction
Introduction
Overview of binary addition and subtraction with examples.
Aim: Explain clearly so no doubts remain.
Binary Addition
Basic Rules
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (2 in decimal)
Result: 0 (place value), Carry: 1
Example:
1 + 1 + 1
1 + 1 = 10 (carry 1)
10 (carry 1) + 1 = 11 (3 in decimal)
Examples
Simple Addition
0 + 0 = 0
1 + 0 = 1
1 + 1 = 10 (carry 1)
Multiple Bits Addition
Example:
1110 (14 in decimal)
+
1100 (12 in decimal)
Steps: Breakdown each bit, apply basic rules, and sum up.
Result:
11010 (26 in decimal)
Fractional Binary Numbers
Start from the rightmost bit (LSB).
Carry forward as needed.
Example conversion: 0.1110 + 0.1100
Decimal equivalent involves powers of 2: 0.75 and 0.375 respectively.
Sum:
1.125
Binary Subtraction
Basic Rules
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1
requires borrowing:
Borrow '1' from the next higher bit.
Subtraction then follows normal rules.
Examples
Simple Subtraction
0 - 0 = 0
1 - 0 = 1
1 - 1 = 0
0 - 1
requires borrowing:
Example conversion: Borrow from the higher bit.
Multiple Bits Subtraction
Example:
1110 (14 in decimal)
-
1010 (5 in decimal)
Steps: Breakdown each bit, borrow where needed, and subtract.
Result:
1001 (9 in decimal)
Complex Scenarios
Involves multiple borrow operations.
Example: larger binary numbers with multiple carry-overs.
Summary of Borrowing
Sequential borrowing if immediate higher bit is 0.
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