Concept Summary

Key Revision Rules & Formulas

• 2's Complement representation is preferred for binary arithmetic because addition and subtraction can use the exact same adder circuit without sign bit branch conditions.
• Booth's Algorithm efficiently multiplies signed 2's complement binary numbers by encoding adjacent bits (01 -> add multiplier, 10 -> subtract multiplier).
• IEEE 754 Single Precision: 32 bits total (1 Sign bit, 8 Exponent bits with Bias 127, 23 Mantissa bits).
• ALU (Arithmetic Logic Unit) executes arithmetic (+, -, *, /) and logical (AND, OR, NOT, XOR) operations.

Common Exam Pitfalls

• Forgetting to add the 127 bias value in IEEE 754 single-precision exponent calculations.
• Assuming 1's complement has a single representation for zero (1's complement has +0 and -0, while 2's complement has unique 0).

Sample Practice Questions