Question 1

Why do computers use binary instead of decimal?

Accepted Answer

Electronic circuits are most reliable with just two distinct states: on (high voltage ≈ 1) and off (low voltage ≈ 0). Representing 10 distinct states for decimal would require much more precise voltage control and would be far more susceptible to electrical noise. Binary's simplicity allows billions of transistors to operate reliably at GHz speeds with billions of operations per second.

Question 2

What is the largest number a byte can hold?

Accepted Answer

A byte (8 bits) can represent 2⁸ = 256 different values. For unsigned integers: 0 to 255. For signed integers (two's complement): −128 to 127. The maximum unsigned byte value in binary is 11111111₂ = 255; in hex it's FF.

Question 3

How do I convert a negative number to binary?

Accepted Answer

Use two's complement: (1) Convert the positive version to binary, (2) Flip all bits (0→1, 1→0), (3) Add 1. Example — −13 in 8-bit: +13 = 00001101₂, flip bits = 11110010₂, add 1 = 11110011₂. This is how all modern computers store negative integers.

Question 4

What is the difference between binary and hexadecimal?

Accepted Answer

Both are positional number systems used in computing. Binary (base-2) uses only 0 and 1 — the native language of computers. Hexadecimal (base-16) uses 0–9 and A–F as a compact notation for binary — every 4 binary digits correspond to exactly 1 hex digit. Hex is used for memory addresses, color codes (#RRGGBB), and machine code because it's more compact and readable than raw binary.

Question 5

What are bitwise operations used for?

Accepted Answer

Bitwise operations (AND, OR, XOR, NOT, shifts) manipulate individual bits within integers. Common uses: bit flags and permissions (Unix chmod), checking even/odd (n & 1), fast multiplication/division by powers of 2 (bit shifting), encryption algorithms, hash functions, CRC error detection, network subnet masks, and game development (compact state storage in a single integer).

Question 6

What is binary floating point and why does 0.1 + 0.2 ≠ 0.3 in programming?

Accepted Answer

Most modern computers use IEEE 754 binary floating point, which represents decimal fractions in binary. Just as 1/3 = 0.3333... cannot be represented exactly in decimal, 1/10 cannot be represented exactly in binary (it's an infinitely repeating binary fraction). This causes tiny rounding errors: in most languages, 0.1 + 0.2 = 0.30000000000000004. Use integer arithmetic (work in cents, not dollars) or decimal libraries for exact financial calculations.

Question 7

How is binary used in data storage and file sizes?

Accepted Answer

Storage is measured in bytes (8 bits), kilobytes (1,024 bytes), megabytes (1,024 KB), gigabytes (1,024 MB), etc. Note: hard drive manufacturers use SI prefixes (1 KB = 1,000 bytes) while operating systems use binary prefixes (1 KiB = 1,024 bytes), causing the apparent "missing space" discrepancy when you buy storage. A 1 TB drive shows ~931 GiB in Windows because 1,000,000,000,000 ÷ 1,073,741,824 ≈ 931.

Question 8

What is binary-coded decimal (BCD)?

Accepted Answer

BCD encodes each decimal digit as a 4-bit binary group: 0=0000, 1=0001, ..., 9=1001. So decimal 93 in BCD is 1001 0011. BCD is used in financial systems (avoids floating-point rounding errors), digital clocks and displays (7-segment displays decode BCD directly), and old mainframe systems. It's less space-efficient than pure binary but eliminates decimal-to-binary conversion errors in critical applications.

Phép Tính	Nhị Phân	Thập Phân Tương Đương
1010 + 0110	10000	10 + 6 = 16
1100 − 0101	0111	12 − 5 = 7
1011 × 0011	100001	11 × 3 = 33
1010 ÷ 0010	0101	10 ÷ 2 = 5

Thập Phân	Nhị Phân	Bát Phân	Thập Lục Phân
0	0000	0	0
5	0101	5	5
10	1010	12	A
15	1111	17	F
16	10000	20	10
255	11111111	377	FF

Máy Tính Nhị Phân

Phép Tính Nhị Phân Là Gì?

Quy Tắc Phép Tính Nhị Phân

Hệ Số và Chuyển Đổi

Câu Hỏi Thường Gặp

Máy Tính Nhị Phân

Phép Tính Nhị Phân Là Gì?

Quy Tắc Phép Tính Nhị Phân

Hệ Số và Chuyển Đổi

Câu Hỏi Thường Gặp

Máy Tính Liên Quan