Number systems / Number conversions

Question 1

What is binary ?

Answer 1

• Binary codes is a type of coding system. Digits 0-1 are used to represent N.Os & letters on a computer system.
• The final form of a binary code is always a 4 digits number of 0s & 1s.

Question 2

What are the binary base numbers?

Answer 2

Base numbers: 128, 64, 32, 16, 8, 4, 2, 1

Question 3

Using ONLY 0-1, what numbers from the binary base numbers would you use to make the n.o 7 ?

Answer 3

128 64 32 16 8 4 2 1
0 0 0 0 0 1 1 1
Binary code: 0111 (4+2+1 =7)

Question 4

What is denary ?

Answer 4

• Denary codes is a type of coding system. Digits 0-9 are used to represent N.Os & letters on a computer system.
• The final form of a denary code is always 8 digits numbers of 0s & 1s.

Question 5

Using the binary base numbers, make the number 5.

Answer 5

128 64 32 16 8 4 2 1
0 0 0 0 0 1 0 1
Denary code: 00000101 (4+1=5)

Question 6

What is a hexadecimal?

Answer 6

Hexidecimal codes is a type of coding system, which is used to convert binary and denary into whole number. the hexadecimal base numbers are used to form the final number.

Question 7

What are the hexadecimal base numbers/letters ?

Answer 7

Base numbers/letter: 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 ,9, A10, B11, C12, D13, E14, F15.

Question 8

Using the hexadecimal base number, write the number 199 in hexadecimal form.

Answer 8

199: 128 64 32 16 8 4 2 1
1 1 0 0 0 1 1 1
Binary = 1100 / 0111 = Denary

1100/0111 : 128 64 32 16 8 4 2 1
Binary: 0 0 0 0 1 1 0 0
Denary: 0 0 0 0 0 1 1 1
1100 = 12 0111 = 7

12/7:0 1 2 3 4 5 6 7 8 9 A10 B11 C12 D13 E14 F15
0 0 0 0 0 0 1 0 0 0 0 1 0 0 0
12/7 in Hexadecimal = C7

Question 9

Using binary and denary, how would you convert C7 into a whole number?

Answer 9

1) C7 = 12/7 in the Hexadecimal base number table.

2) CONVERT TO BINARY
C7 - C =12 / 7=7
Base N.Os: 128 64 32 16 8 4 2 1
12: 0 0 0 0 1 1 0 0
7: 0 0 0 0 0 1 1 1
Binary = 1100 / 0111

3)COVERT TO DENARY
Base N.Os: 128  64  32  16  8  4  2  1
                       1      1    0    0   0  1  1  1
128+64+4+2+1= 199
Denary = 199.