تكنولوجيا المعلومات والاتصالات (بالإنجليزية) الصف الثالث الثانوي، الأسبوع 5: Hexadecimal to binary: four bits for each symbol

Hexadecimal and binary together

الأسبوع 5 · الوحدة ١ «النظم العددية» (٥): مثال آخر على التحويل إلى السداسي عشر، ومن السداسي عشر إلى الثنائي ومن الثنائي إلى السداسي عشر · 3 دروس

Hexadecimal to binary: four bits for each symbol

ICT Secondary 3 Term 1, Unit 1, Topic 1: pp. 22–26

GoalConvert hexadecimal to binary symbol by symbol.

New words

group of four bits · the 4 bits that stand for one hexadecimal symbollookup table · a table you read the answer from; here 16 rows, symbol and four bitsleading zeros · zeros at the left end of a number; they may be dropped only at the very start of the whole answer

Explanation

Because 16 = 2×2×2×2, one hexadecimal symbol is exactly four bits. To convert hexadecimal to binary, replace each symbol by its group of four bits from the lookup table and put the groups side by side. Every group must have four bits, so write zeros on its left when needed: 7 is 0111, not 111. At the end you may drop the zeros at the very start of the whole answer, but never the zeros inside it. For example (3B)₁₆ is 0011 for the 3 and 1011 for the B, so 00111011, and without the leading zeros (111011)₂, which is 59.

Hexadecimal	Four bits	Decimal
0	0000	0
1	0001	1
2	0010	2
3	0011	3
4	0100	4
5	0101	5
6	0110	6
7	0111	7
8	1000	8
9	1001	9
A	1010	10
B	1011	11
C	1100	12
D	1101	13
E	1110	14
F	1111	15

Worked examples

Symbol	9	C	0
Four bits	1001	1100	0000

Convert (9C0)₁₆. The 9 is 1001, the C is 1100 and the 0 is 0000. The answer is 100111000000: the zeros inside it must stay, and here there are none to drop at the start.

Symbol	7	F
Four bits	0111	1111

Convert (7F)₁₆. The 7 is 0111 and the F is 1111, so 01111111. The first 0 is at the very start of the whole answer and can be dropped: (1111111)₂, which is 127.

Class activity

Write the 16-row table from memory, from 0000 for 0 up to 1111 for F. Then use it to convert (D4)₁₆ and (2F5)₁₆ to binary.

Practice

Convert (A5)₁₆ to binary.

Convert (B2)₁₆ to binary.

Convert (100)₁₆ to binary.

A hexadecimal number has 6 symbols. How many bits does it stand for, keeping all the zeros?

Why do we write 7 as 0111 inside a longer answer?