Computer Architecture and Organization Fundamentals

Computer Architecture vs. Computer Organization

IEEE 754 Floating Point Bias

• Single Precision (32-bit): Bias = 127 (2⁷ - 1)
• Double Precision (64-bit): Bias = 1023 (2¹⁰ - 1)

Why Bias is Used

Bias allows storing both positive and negative exponents using only unsigned integers. Instead of storing the actual exponent, we store (exponent + bias), which is always positive. This simplifies the comparison of floating-point numbers.

Cache Memory Performance

Hit Ratio and Effective Access Time

Hit Ratio (h): The ratio of the number of successful cache accesses (hits) to total memory accesses.

h = Number of Hits / Total Accesses

Effective Access Time (EAT) Formula:

EAT = h × Tc + (1-h) × (Tc + Tm)

Simplified: EAT = Tc + (1-h) × Tm

Where: Tc = Cache access time, Tm = Main memory access time

Direct Memory Access (DMA)

DMA (Direct Memory Access): A technique that allows I/O devices to transfer data directly to or from memory without CPU involvement. The DMA controller takes control of the system bus and handles the transfer.

Three Modes of DMA Operation

• Burst Mode: DMA takes complete bus control until the entire transfer is done.
• Cycle Stealing Mode: DMA steals one bus cycle at a time, transferring one word per steal.
• Transparent Mode: DMA uses the bus only when the CPU is not using it.

Carry Look-ahead Adder (CLA)

In a Carry Look-ahead Adder:

• Generate (G_i) = A_i · B_i — Carry is generated when both inputs are 1.
• Propagate (P_i) = A_i ⊕ B_i — Carry is propagated when exactly one input is 1.
• Sum: S_i = P_i ⊕ C_i
• Carry: C_i+1 = G_i + P_i · C_i

Booth's Algorithm Multiplication

Task: Multiply (-7) × (+5) using 5-bit representation.

Given: Multiplicand M = +5 = 00101, Multiplier Q = -7 = 11001 (2's complement)

Setup: -M = 11011, n = 5 bits