Binary/conversions

denary = decimal(0,1,2,3….9-whole numbers not math decimals).Denary has base of 10

binary only does 1 and 0

here binary = 11100000 so since there's a 128 and a 64 and a 32 the decimal value would 128 + 64 + 32=224

Hexadecimal Conversions

Hexadecimal to binary

hexadecimal uses number system uses base of 16 where the 8 bits are 4 bits 1-8 twice(10000000=80)

since we only have ten digits 0-9 in our system the additional six number 10-15 in the hexadecimal system are represented by the letters A-F e.g.10110001=B1 (but the numbers from 0-9 are the same e.g. 10001000=88)

  • A = 10

  • B = 11

  • C = 12

  • D = 13

  • E = 14

  • F = 15

To convert a hexadecimal number to binary, each hexadecimal digit is replaced by its corresponding four-digit binary equivalent.

Hexadecimal to denary

as hexadecimal has a base of 16 as oppose do denary number system that has a base of 10

this means that instead of 1s and 10s you use 1s and 16s

Multiply the hexadecimal digits by their column place values 16 and 1 then add the results e.g. 5B = 5 × 16 and B x 1(B=11) = 80 + 11 = 91 in denary so B9=91

to convert denary to hexadecimal you just need to divide the whole number by 16 then work out the remainder that will be the second digit e.g. 91/16=5 remainder 11(remember 11=B) so the answer is 5B

Binary shifts

a binary shift moves all of the bits in a given binary number either to the left or the right by a given number of spaces. All empty spaces are filled with zero

Effects of shifts:

In a left binary shift, the value of the number is effectively multiplied by two for each position moved, while a right binary shift divides the number by two, rounding down if necessary. Similarly a left shift in denary multiplies the number by 10

if you're doing a left shift of 4 on an 8-bit number and the result must also remain 8 bits, you simply shift left and discard any bits that go past 8 bits (overflow), then fill the right with 0s. if not done the number would overflow and more than 8 bits would be needed for the result which is greater than 255(1 byte-8 bits).