Integer Arithmetic
The document discusses integer arithmetic in computers including integer representation, multiplication, and division. It explains how multiplication is done by taking the partial products of each digit and adding them together. An example of multiplying two binary integers in shown. Negative number multiplication is also discussed along with two solutions: converting to positive numbers before multiplying or using Booth's algorithm. Division is described as more complex than multiplication, especially with negative numbers, as it is based on the principle of long division. An example of unsigned binary integer division is demonstrated step-by-step showing the quotient, dividend, remainder, and partial remainders. References for further reading are also provided.
Integer Arithmetic
- 1. Organisasi dan Arsitektur Komputer Ajeng Savitri Puspaningrum, M.Kom Pertemuan 14
- 3. Learning computer arithmetic Learning integer representation
- 4. Multiplication Complex Work out partial product for each digit Take care with place value (column) Add partial products
- 5. Multiplication Example 1011 Multiplicand (11 dec) x 1101 Multiplier (13 dec) 1011 Partial products 0000 Note: if multiplier bit is 1 copy 1011 multiplicand (place value) + 1011 otherwise zero 10001111 Product (143 dec) Note: need double length result
- 6. Multiplying Negative Numbers This does not work! Solution 1 Convert to positive if required Multiply as above If signs were different, negate answer Solution 2 Booth’s algorithm
- 7. Division More complex than multiplication Negative numbers are really bad! Based on long division
- 8. Division of Unsigned Binary Integers 001111 1011 00001101 10010011 1011 001110 1011 1011 100 Quotient Dividend Remainder Partial Remainders Divisor
- 9. Refference Stalling, William, Computer Organization and Architecture, 10th Edition, Pearson, 2015 Abdurohman, Maman, Organisasi dan Arsitektur Komputer revisi ke-4, Penerbit Informatika, 2017