2.6 Hexadecimal and binary

Question 1

converting binary to hexadecimal

Answer 1

• split the 8 bit byte into two 4 bit nibbles
• convert the bits in each nibble into denary numbers using the place values
• add these together to give the hexadecimal

Question 2

converting hexadecimal to binary

Answer 2

• each hexadecimal digit is converted to denary
• each denary number is converted into a nibble
• the nibbles are combined

Question 3

use of hexadecimal

Answer 3

• used to help humans cope with long strings of binary digits as they are shorter in hexadecimal
• MAC addresses are given in hexadecimal form
• when a computer malfunctions, error code numbers are given in hex
• hex is also used to represent numerical values in assembly language

Question 4

true colour and hex

Answer 4

true colour uses 24 bits to code every available colour variation, 2[24] = 16 777 216 (over 16 mill)

each one is represented by three 8 bit numbers that can be simplified to three 2-digit hexadecimal ones

it is easier to remember and enter the hexadecimal number than the 24 digit binary number

Question 5

Convert the bit pattern 10110111 into hexadecimal. [1]

Answer 5

B7

Question 6

Convert the hexadecimal number E9 into a binary number. You must show your working. [2]

Answer 6

11101001