Computer Org 2019.01.29

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Qwickly Attendance: 8850

Unsigned: Using all of the bits

Positive integers are represented by strings of binary digits - of fixed length given by the word length

Numbers in the range of 0 to 2^32-1 can be represented

The left most bit is the most significant because it has the highest value. The right most bit has the lowest value. Think of a bank account.

Do C++ sizeof(int)

Arithmetic:

Binary arithmetic, addition and subtraction are similar to decimal

A fundamental issue on a computer is the fixed word size

If you have five bits, the largest integer you can represent is 31

The operands and result is the dependent on the word length, and sometimes the result will be too small (negative) or too large (positive) to be represented.

The largest five bit number is 15 and you are left with 4 bits (1,2,4,8). The smallest of five bits is -16.

How to add binary numbers:

Consider adding two 1-bit binary numbers x and y

0+0 = 0

0+1= 1

1+0 = 1

1+1 = 10

Half Adder (See slides)

Full Adder

Transistors are all enclosed in an "IC" or integrated circuits

Circuit Design & Logic Conversion and Construction:

Circuit Design Goals:

To reduce cost (goal) ..

Use the same kind of gates

To reduce size. Size is heat. Size is money. Size is... bigger!

Minimize the number of gates

Challenge:

Turn any circuit into all NORS, or all NANDS