CS: Hexadecimal Numbers: Base 16 Explained
Practice reading, converting, and using base 16 numbers
CS: Hexadecimal Numbers: Base 16 Explained
Practice reading, converting, and using base 16 numbers
CS - Grade 6-8
- 1
Hexadecimal is a base 16 number system. List all 16 symbols used in hexadecimal, in order from smallest to largest.
After 9, hexadecimal uses letters instead of making a new two-digit number.
The 16 hexadecimal symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. The letters A through F stand for decimal values 10 through 15. - 2
Write the decimal value of each hexadecimal digit: A, B, C, D, E, and F.
A equals 10, B equals 11, C equals 12, D equals 13, E equals 14, and F equals 15 in decimal. - 3
Convert the hexadecimal number 2F to decimal. Show the place values you used.
In a two-digit hexadecimal number, the left digit is in the 16s place and the right digit is in the 1s place.
The hexadecimal number 2F equals 47 in decimal. The 2 is in the 16s place, so it is worth 2 x 16 = 32, and F is worth 15, so 32 + 15 = 47. - 4
Convert the hexadecimal number 3A to decimal.
The hexadecimal number 3A equals 58 in decimal. The 3 is worth 3 x 16 = 48, and A is worth 10, so 48 + 10 = 58. - 5
Convert the hexadecimal number 7C to decimal.
Remember that C represents 12 in hexadecimal.
The hexadecimal number 7C equals 124 in decimal. The 7 is worth 7 x 16 = 112, and C is worth 12, so 112 + 12 = 124. - 6
Convert the decimal number 26 to hexadecimal.
Divide by 16 to find the left digit, then write the remainder as the right digit.
The decimal number 26 equals 1A in hexadecimal. One group of 16 fits into 26 with 10 left over, and 10 is written as A. - 7
Convert the decimal number 63 to hexadecimal.
The decimal number 63 equals 3F in hexadecimal. Three groups of 16 make 48, and 63 - 48 = 15, which is written as F. - 8
Convert the decimal number 100 to hexadecimal.
Check your answer by multiplying the left digit by 16 and adding the right digit.
The decimal number 100 equals 64 in hexadecimal. Six groups of 16 make 96, and 100 - 96 = 4, so the hexadecimal number is 64. - 9
Complete the table by converting each 4-bit binary value to one hexadecimal digit: 0000, 0001, 1010, 1111.
A 4-bit group can represent decimal values from 0 to 15.
The conversions are 0000 = 0, 0001 = 1, 1010 = A, and 1111 = F. Each group of 4 binary bits can be written as one hexadecimal digit. - 10
Convert the binary number 1101 0110 to hexadecimal by grouping the bits into two 4-bit groups.
The binary number 1101 0110 equals D6 in hexadecimal. The group 1101 is 13, which is D, and the group 0110 is 6. - 11
Convert the hexadecimal number 4B to binary. Write each hexadecimal digit as 4 bits.
Each hexadecimal digit becomes exactly 4 binary bits.
The hexadecimal number 4B equals 0100 1011 in binary. The digit 4 is 0100, and B is 1011. - 12
A web color is written as #FF0000. In this format, the first two hexadecimal digits are red, the next two are green, and the last two are blue. Which color channel has the highest value?
FF is the largest two-digit hexadecimal value, and 00 is the smallest.
The red channel has the highest value. In #FF0000, red is FF, while green is 00 and blue is 00, so the color is full red with no green or blue. - 13
A memory address is written as 0x1C. The prefix 0x means the number is hexadecimal. What is 0x1C in decimal?
The address 0x1C equals 28 in decimal. The 1 is worth 16, and C is worth 12, so 16 + 12 = 28. - 14
Choose the larger value: hexadecimal 2A or decimal 35. Explain your answer.
Convert the hexadecimal number to decimal before comparing.
Hexadecimal 2A is larger. Hexadecimal 2A equals 2 x 16 + 10 = 42 in decimal, and 42 is greater than 35. - 15
A byte is 8 bits, and it can be written as two hexadecimal digits. What is the largest value of one byte in hexadecimal, and what is that value in decimal?
The largest value of one byte is FF in hexadecimal, which equals 255 in decimal. The first F is worth 15 x 16 = 240, and the second F is worth 15, so 240 + 15 = 255.