# Lecture 01

#### What is a sequential program?

Single threaded, only one thing going on at a time.

#### Goal: Foundations

Understand how sequential programs "work" from the ground up

#### Starting Point

Bare hardware (so to speak)

For CS 241, bare hardware is simulated MIPS machine which only understand 1 and 0

#### At the end

Get programs written in a C-like language to run on MIPS

## The beginning: Binary and Hexadecimal Numbers

### Bit

Binary digit, i.e. 0 or 1 (high/low voltage, configurations on magnetic tape)

• all the computer understands
• convenient to group bits together

### Byte

8 bits, e.g. 11001010, 256 possible bytes

### Word

Machine specific grouping of bytes

• we will assume a 32-bit computer architecture
• 1 word = 32 bits = 4 bytes

4 bits (1/2 a byte) sometime called a nibble

### 1. A number

Binary number system. 11001001 = 201

#### How can we represent negative numbers?

Simple way: reserve the first bit to represent the sine: o for +, 1 for -. e.g. the 11001001 = -73

But: two representation for 0: 00000000, 100000000 - wasteful - arithmetic on numbers is tricky (e.g. add a positive number and a negative number)

Better way: 2's Complement Notation

1. Interpret the n-bit numbers on unsigned integer
2. If the first bit is 0, done.
3. else subtract $$2^n$$

E.g. for n = 3

|000|001|010|011|100|101|110|111|
|  0|  1|  2|  3| -4| -3| -2| -1|

n bits represent numbers $$-2^{n-1}$$~$$2^{n-1}-1$$

• only one 0
• left bit gibes sign
• additions is clean - just module $$2^n$$
• same addition circuitry works for signed and unsigned

Then 11001001 = 201-256 = -55

• base 16, 0...F
• more complication binary
• each hex digit = 4 bit (1 nibble)
• 11001001 = 0xC9

#### A: We cannot, Need to remember what our intent was when we stored the byte!

We do not know for sure that 11001001 represents a number!

### 2. A character- which character?

Need conventional mapping between bit patterns or characters

#### ASCII

• uses 7 bits
• 8 bit can be used for additional chars
• non-standard compatibility issues

11001001 is not 7-bit ASCII. 100101 decimal 73 is ASCII for I

### 3. An instruction (or part for one)

• For us, instructions are 32 bits=4bytes
• 11001001 could be part of an instruction