Binary to Decimal Conversion Explained
This explanation details how to convert a binary number to its decimal equivalent. Binary is a base-2 system, using only digits 0 and 1, while decimal is a base-10 system.
Understanding Positional Value
In the binary number 110, each digit holds a specific positional value, which is a power of 2. Starting from the rightmost digit:
- The rightmost digit (0) is in the $2^0$ (ones) place.
- The middle digit (1) is in the $2^1$ (twos) place.
- The leftmost digit (1) is in the $2^2$ (fours) place.
Calculating the Decimal Value
To find the decimal equivalent, multiply each binary digit by its corresponding positional value and sum the results.
For the binary number 110:
Decimal Value = ($1 \times 2^2$) + ($1 \times 2^1$) + ($0 \times 2^0$)
| Binary Digit | Positional Value (Power of 2) | Calculation |
|---|---|---|
| 1 | $2^2$ = 4 | $1 \times 4 = 4$ |
| 1 | $2^1$ = 2 | $1 \times 2 = 2$ |
| 0 | $2^0$ = 1 | $0 \times 1 = 0$ |
Summing the results from the calculation:
Decimal Value = $4 + 2 + 0 = 6$
Final Conversion Result
Therefore, the binary number 110 is equivalent to the decimal number 6.
Important Questions from Binary Number System
Convert decimal number 26.85 into binary equivalent.
- If $(L)_M$ represents a number L in base-M number system, then identify the correct descending order of the following numbers A-D when converted to decimal number system.
A. $(20003.2)_4$
B. $(111111.11)_2$
C. $(732.2)_8$
D. $(C2.6)_{16}$
Choose the correct answer from the options given below : Given below are two statements with reference to different number systems:
Statement I: (D6C1)16 = (54977)10
Statement II: (41819)10 = (A35B)16
In the light of the above statements, choose the correct answer from the options given below:An Indian company designs a mobile application to process staff records. In each record, 10 bits are used to store staff ID and 20 bytes are used to store staff names. How many staff records can the mobile application support?
Match List I with List II
LIST I (Statement) List II (Value) A. Number of bytes formed from 8 bits I. 6 B. Base-10 (denary) value of the binary number : 110 II. 4 C. If there are 2ᴾ bytes in 1 mega byte, then what is the value of P ? III. 1 D. An ISP company advertises its broadband download speed as 128 mega bits per second. How many 4-mega byte files can be downloaded per second using the company's broad band? IV. 20 Choose the correct answer from the options given below:
