Conversions of number systems

Question 1

Binary to Denary

Answer 1

Classic conversion, 128 halving down to 1, above each digit in binary, then add all the values above the 1’s.
128 64 32 16 8 4 2 1
1. 0. 1. 1.1 0 1 1
1+2+8+16+32+128 = 187

Question 2

Denary to binary

Answer 2

Also classic number scale. Write out 128 to 1 scale, subtracting the largest possible number from the scale, leaving a 1 if you subtracted, 0 if not.
209
128 64 32 16 8 4 2 1
1 1 0 1 0 0 0 1
209-128=81 81-64=17 17-16=1. 1-1=0
11010001

Question 3

Binary to hexadecimal

Answer 3

Split the 8 bit binary number into 2 4 bit nibbles. Work out decimal for each one, and give them a value based on hex scale. 0-9 = 0-9, 10-15 = A-F

Question 4

Hex to binary

Answer 4

Opposite of before. Just work out what each hex character refers to in decimal, then convert them to binary and stick them together.

Question 5

Denary to hex

Answer 5

Just convert to binary, then convert binary to hex

Question 6

Hex to denary

Answer 6

Just convert hex to binary, then binary to denary