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# ItC Week 7 - ALU

###### tags: `Intro_to_Comp`

- ## Introduction

- Digital Building Blocks
- gates, multiplexer, decoder, register etc.

- ## Arithmetic Circuits & Number Systems

- 1-bit Half Adder & Full Adder
- full adder handles carry-ins
- **Multibit adder**
- **Ripple carry adder**
- really slow
- $t_{ripple} = N t_{FA}$
- can be accelerated with parallelizing computation
- e.g. divide a 16-bit number into 4 blocks of 4-bit numbers
- **Carry-lookahead Adder**
- take advantage of *generate* and *propagate* signals
- *generate* : $G_{i} = A_i B_i$
- *propagate* : $P_i = A_i +B_i$
- *carryout* : $C_i = G_i + P_i C_{i-1}$
- how to add
1. Compute $G_i$ and $P_i$
2. Compute $G$ and $P$ for the block
3. $C_{in}$ of the number propagate through each block
- $t_{CLA}=t_{pg}+t_{pg\_block}+$
- Subtracter
- $Y = A-B =A+B'+1$
- Comparator (Equality)
- XOR gate and NOT gate
- Comparator (less than)
- use subtracter's output's sign bit
- **ALU**
- combines multiple numerical and logical operations into a single unit
- inside CPU, GPU, FPU...
- two number inputs $A$ & $B$
- a input $F$ to decide which calculation result to output
- Shifter
- **Logical Shifter**
- **Arithmetic Shifter**
- **Rotator**
- **Multiplier**
- realized with AND gates and shifters
- **Integers**
- Positive Numbers
- unsigned binary
- Negative Numbers
- 2's complement
- sign/magnitude
- **Fractions**
- fixed point
- binary point fixed
- e.g. 2's complement, sign/magnitude
- **Floating Point**
- $\pm M \times B^E$
- Mantissa, Base, Exponent
- Ver. 1
- 1 bit sign + 8 bits exponent + 23 bits mantissa
- Ver. 2
- since every mantissa starts with "1", don't store it
- 23 bits mantissa $\to$ 23 bits "fraction"
- Ver. 3 (IEEE 754 standard)
- add support for negative exponents
- exponent $\to$ "biased" exponent (+0x7F)
- Addition
1. extract
- Counter
- +1 on each clock edge
- Shift Register

- ## Sequential Building Blocks

- ## Memory Arrays

- Memory types
- DRAM : Dynamic Random Access Memory
- SRAM : Static Random Access Memory
- ROM : Read Only Memory
- N address bits & M address bits
- 
- DRAM vs SRAM
- DRAM uses capacitor
- SRAM uses cross-coupled inverters
- DRAM is computer's memory sticks (8 ~ 16GB)
- SRAM is used in CPU's caches (L3 Cache 32 ~ 64MB)

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