1.1 number systems

what are number systems

determines how values are represented using digits

what does a number base do

defines the number of unique digits used in that system

what is denary

they are used by humans for counting, they are base 10.

what is binary

they are used by computers to represent all data and instructions, they are base 2.

what is hexadecimal

they are used by programmers to compact the representation, they are base 16.

how would you convert binary to denary (example 10110010)

128 + 32 + 16 + 2 =178

how would you convert denary to binary

make sure the ones in the binary is added up to the denary number

how would you convert binary to hexadecimal

split byte into nibble and convert each nibble into denary and convert into hexadecimal

A= 10

B = 11

C = 12

etc.

how would you convert hexadecimal to binary

split each hexadecimal digit and convert into denary then binary then put all binary code together.

why is hexadecimal used

easier for people to read and takes less time to type the binary, and is shorthand representation of binary.

what two examples do people used hexadecimal for

colour codes - hexadecimal used to represent the RGB colours values in HTML

Media access control address - devices on a network have a unique media access control address written in hexadecimal

what are the rules of binary addition

1 + 0 = 1 (no carry)

0 + 0 = 0 (no carry)

0 + 1 = 1 (no carry)

1 + 1 = 0 (carry one)

1 + 1 + 1 = 1 (carry one)

where do we shift the binary when dividing

right shift

where do we shift the binary when multiplying

left shift

what is 2s complement

representing negative numbers

what is the process of 2 complement

flip all binary 0 to 1 and 0 to 1

add one