Binary Arithmetic
Module 8
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Reading Assignment Sec. 4-1
– 4-4: pp. 149-165 |
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Supplemental Material |
Arithmetic
Operations
- Addition
- Basic rules
- Unsigned binary addition
- Subtraction
- Basic rules
- Signed magnitude
- Is there a better way?
- Two's
compliment versus unsigned binary
- X - Y = X + (-Y)
- Subtraction now becomes addition
- Examples
- Overflow
- Unsigned and two's complement arithmetic
- add two positives and get negative
- add two negatives and get positive
- no errors with mixed addition
Implementation
- Implementation
of a single bit adder
- Adder truth table
- Half adder
- Carry out, carry in and the full adder
- Gate level implementation
- Implementation
of a single bit subtractor using two's complement
- Modify the full adder to negate one of the
inputs
- Set the carry in
Adder/Subtractor
- Construction
of 32-bit ripple carry adder from full adder components
- Maximum latency is 2n+2 gate delays
- Inclusion
of subtraction via logic for negation of an operand
- Generation
of zero, carry, overflow. and negative condition codes
- Carry
look-ahead adder
- Logarithmic delay
- Binary
multiplication
- Number of bits of the result: m-bit x n-bit number gives an m+n
bit number
- Multiplication as successive addition of shifted
partial products