cs - base conversions, logic gates

digital values are ____

discrete

binary:

1 represents a ___ ____

0 represent a ____ _____

1 - high voltage

0 - low voltage

how to convert binary to denary

• Starting from the rightmost digit (least significant bit), assign powers of 2.

  • The rightmost bit is 202^020, the next is 212^121, then 222^222, and so on.

• Multiply each binary digit (0 or 1) by its corresponding power of 2.

  • Add up all the results.
    
    
    

convert 10110110 into denary

how to convert denary to binary (small numbers) e.g. 15

1. write out powers of 2

2. write 1 under biggest power that can fit into denary number

3. same for remainder

how to convert denary to binary (larger numbers) e.g.185

1. by 2 and note the remainders:

2. Write the remainders from bottom to top

convert 228 into binary

write out conversion table for den/hex/bin

how to convert hex to denary (by positional value) e.g. 38B

how to convert hex to binary (by positional value) e.g. 38B

how to convert binary to hex (by nibbles) e.g. 011111010010

how to convert denary to hex e.g. 23

• Divide 23 by 16:

  • 23÷16=1 remainder 7.

  • (7÷ (16^0 so 1)) = 7

• Write the result:

  • Quotient = 1, Remainder = 7.

• Combine the digits: 17 (Hexadecimal).

how to convert denary to hex e.g. 458

1. write out powers of 16, as many digits as denary number

2. how many 16² fit into 458, 458÷256 = 1, remainder 202

3. how many 16¹ fit into 202, 202÷16 = 12, remainder 10

4. so you have 1, 12 (C in hex), and 10 (A in hex)

5. 1CA

binary addition rules (each combo for 1, 0)

• 0 + 0 = 0

• 1 + 0 = 1

• 1 + 1 = 10

• 1 + 1 + 1 = 11

carry over

4 reasons to use hex

• less display space, faster to enter data (16 bytes as just 4 hex digits)

• EASIER to identify values

• EASIER to spot errors

• (more human friendly)

• easier to convert back to binary if necessary

4 uses of hex

• colour coding e.g #FFFFF

• low level programming (e.g. assembly): quicker, easier, less error prone

• addresses: both IP and MAC (IPv6 uses hex)

• error messaging: in embedded systems e.g. lifts, bc hex takes up less screen space than long binary strings

what are the 4 logic gates

NOT
AND
OR
XOR

NOT gate symbol and truth table

AND gate symbol and truth table

OR gate symbol and truth table

at least one:

XOR gate symbol and truth table

Exclusive or (only 1)