Chapter 4: Arithmetic for Computers
1: Concepts Introduced in Chapter 4
2: Binary Numbers
3: Binary Representations
4: Sign and Zero Extension
5: Two's Complement Negation
6: Bases That Are a Power of Two
7: Examples of Converting between Bases
8: 4.3: Binary addition, showing carries from right to left.
9: Subtraction by Negating and Adding
10: Detecting Overflow
11: Floating-Point Values
12: Normalized Floating-Point Values
13: IEEE Floating-Point Standard
14: Interpreting the IEEE FPS
15: Example of Representing a Value in IEEE FPS
16: Example of Determining What Value an IEEE FPS Pattern Represents
17: What is the Largest Representable IEEE FPS Value?
18: Boolean Algebra
19: Figure 4.8: Four hardware building blocks used to construct an arithmetic unit.
20: Writing A Logic Equation from a Truth Table
21: Figure 4.9: The 1-bit logical unit for AND and OR.
22: Figure 4.10: A 1-bit adder.
23: Figure 4.11: Input and output specification for a 1-bit adder.
24: Figure 4.17: (Top) A 1-bit ALU that performs AND, OR, and addition on a and b or not(b), and (bottom) a 1-bit ALU for the most significant bit.
25: Figure 4.19: The final 32-bit ALU.
26: Carry-Lookahead AdderF
27: Figure 4.22: A plumbing analogy for carry lookahead for 1 bit, 2 bits, and 4 bits using water, pipes, and valves.
28: script.html#carrylookahead2 Carry-Lookahead Adder (cont.)
29: Figure 4.24: Four 4-bit ALUs using carry lookahead to form a 16-bit adder.
30: Integer Multiplication
31: Figure 4.32: The third multiplication algorithm.
32: Figure 4.33: Multiply example using third algorithm in Figure 4.32.
33: Booth's Algorithm for Multiplication
34: Integer Division
35: Figure 4.40: The third division algorithm has just two steps.
36: Figure 4.42: Division example using third algorithm in Figure 4.40.
37: General Forms of a MIPS Integer Multiply or Divide Instruction
38: Fallacies
