Computer Org. 2019.01.18

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In binary start from right to left

Only add the numbers that are "1" and not "0"

Start at 0 in Binary.

Example: 0 - 9 for Base 10

Binary Addition of 1 bit. 1+0 = 0+1 = 1

(See slide)

Binary Addition (slides)

There are 32 distinct numbers you can get out of 5 bits

In C++ its possible to say: unsigned int x=743;

This means use all the bits there are to represent 743 and no implementation to represent positive or negative, its going to be positive.

Negative numbers. Idea #1: Sign & Magnitude

High bit = 0 means 'positive'

High bit = 1 means 'negative'

Problem 1: We have two zeros.. that is wasteful.

Problem 2: Math doesn't work easily

Negative numbers. Idea #2: '2s Complement'

Harder to understand but more efficient

1 is still a flag that # is negative

One zero +0

Removing the extra zero, -0 now allows for one more negative number (-16)

Will be on exam:

The largest number you can find in a 5 bit signed integer is 15

The smallest number in a 5 bit signed integer is -16

Unsigned: Not losing the top bit

Quiz next week on Binary

When there are three ones in a column you will carry one over

When there are two ones you will carry the one to the next column

Don't be confused. You are adding one to the flipped bits to show that it is now negative. (Example: Slide 39)

How to Negate a Number:

Step 1: Flip all the bits (also called 1’s Complement).

0 becomes 1

1 becomes 0

Step 2: Add 1

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What's wrong with Binary:

Humans are poor at remembering long strings of 1s and 0s

Headaches! Errors!

Make it simpler with 'shorthand' notations (we can have an easier way to write it down):

Hexadecimal (Base 16)

Octal (Base 8)

Hex(hexadecimal) is Base 16:

Represents groups of 4 bits

Use ‘alphabet’ of 0-9 AND a-f to create 16 ‘hex digits’, using 1 char

Ended on slide