Convert the following binary numbers to decimal equivalent. (a) 100 (b) 11010 (c) 10110010 (d) 1.001 (e) 110100.010011 (f) 11010.10110 (g) 1000001.111 Convert Binary 1111 1111 to Hexadecimal Convert Binary 1011 0010 to Hexadecimal Convert Binary 0101 0101 to Hexadecimal Convert Binary 1011 0000 to Hexadecimal Convert Binary 1101 1111 to Hexadecimal Q.2: Convert the following decimal numbers to binary equivalent. (a) 16 (b) 247 (c) 962 (d) 00132 (e) 6 Q3. Convert 18 \times 24 to binary form Convert 23+12 to binary form Short Questions Write the short answers of the following: Q.1: Define Binary Number. Q.2: Define Octal numbers. Research on google please Q.3: Define Decimal number. Q.4: Convert binary number 101012 to decimal numbers. Q.5: Convert binary numbers 111112 to decimal numbers. Q.6: Convert 110011.112 to decimal numbers.
The Correct Answer and Explanation is:
Binary to Decimal Conversion
- (a) 100
In binary, 100 represents:
1×22+0×21+0×20=41 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 41×22+0×21+0×20=4
So, the decimal equivalent is 4. - (b) 11010
In binary, 11010 represents:
1×24+1×23+0×22+1×21+0×20=16+8+2=261 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 16 + 8 + 2 = 261×24+1×23+0×22+1×21+0×20=16+8+2=26
So, the decimal equivalent is 26. - (c) 10110010
In binary, 10110010 represents:
1×27+0×26+1×25+1×24+0×23+0×22+1×21+0×20=128+32+16+2=1781 \times 2^7 + 0 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 128 + 32 + 16 + 2 = 1781×27+0×26+1×25+1×24+0×23+0×22+1×21+0×20=128+32+16+2=178
So, the decimal equivalent is 178. - (d) 1.001
In binary, 1.001 represents:
1×20+0×2−1+0×2−2+1×2−3=1+0+0+0.125=1.1251 \times 2^0 + 0 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} = 1 + 0 + 0 + 0.125 = 1.1251×20+0×2−1+0×2−2+1×2−3=1+0+0+0.125=1.125
So, the decimal equivalent is 1.125. - (e) 110100.010011
In binary, 110100.010011 represents:
Integer part:
1×25+1×24+0×23+1×22+0×21+0×20=32+16+4=521 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 0 \times 2^0 = 32 + 16 + 4 = 521×25+1×24+0×23+1×22+0×21+0×20=32+16+4=52
Fractional part:
0×2−1+1×2−2+0×2−3+0×2−4+1×2−5+1×2−6=0.25+0.03125+0.015625=0.2968750 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 0 \times 2^{-4} + 1 \times 2^{-5} + 1 \times 2^{-6} = 0.25 + 0.03125 + 0.015625 = 0.2968750×2−1+1×2−2+0×2−3+0×2−4+1×2−5+1×2−6=0.25+0.03125+0.015625=0.296875
So, the decimal equivalent is 52.296875. - (f) 11010.10110
In binary, 11010.10110 represents:
Integer part:
1×24+1×23+0×22+1×21+0×20=16+8+2=261 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 16 + 8 + 2 = 261×24+1×23+0×22+1×21+0×20=16+8+2=26
Fractional part:
1×2−1+0×2−2+1×2−3+1×2−4+0×2−5=0.5+0.125+0.0625=0.68751 \times 2^{-1} + 0 \times 2^{-2} + 1 \times 2^{-3} + 1 \times 2^{-4} + 0 \times 2^{-5} = 0.5 + 0.125 + 0.0625 = 0.68751×2−1+0×2−2+1×2−3+1×2−4+0×2−5=0.5+0.125+0.0625=0.6875
So, the decimal equivalent is 26.6875. - (g) 1000001.111
In binary, 1000001.111 represents:
Integer part:
1×26+0×25+0×24+0×23+0×22+0×21+1×20=64+1=651 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 64 + 1 = 651×26+0×25+0×24+0×23+0×22+0×21+1×20=64+1=65
Fractional part:
1×2−1+1×2−2+1×2−3=0.5+0.25+0.125=0.8751 \times 2^{-1} + 1 \times 2^{-2} + 1 \times 2^{-3} = 0.5 + 0.25 + 0.125 = 0.8751×2−1+1×2−2+1×2−3=0.5+0.25+0.125=0.875
So, the decimal equivalent is 65.875.
Binary to Hexadecimal Conversion
- Binary: 1111 1111
Group into 4-bit sections: 1111 1111
Hexadecimal: F F
So, the hexadecimal equivalent is FF. - Binary: 1011 0010
Group into 4-bit sections: 1011 0010
Hexadecimal: B 2
So, the hexadecimal equivalent is B2. - Binary: 0101 0101
Group into 4-bit sections: 0101 0101
Hexadecimal: 5 5
So, the hexadecimal equivalent is 55. - Binary: 1011 0000
Group into 4-bit sections: 1011 0000
Hexadecimal: B 0
So, the hexadecimal equivalent is B0. - Binary: 1101 1111
Group into 4-bit sections: 1101 1111
Hexadecimal: D F
So, the hexadecimal equivalent is DF.
Decimal to Binary Conversion
- (a) 16
16 in binary is 10000. - (b) 247
247 in binary is 11110111. - (c) 962
962 in binary is 1111000010. - (d) 132
132 in binary is 10000100. - (e) 6
6 in binary is 110.
Other Conversions
- Convert 18 × 24 to binary form
18×24=43218 \times 24 = 43218×24=432
432 in binary is 110110000. - Convert 23 + 12 to binary form
23+12=3523 + 12 = 3523+12=35
35 in binary is 100011.
Short Answers
- Binary Number:
A binary number is a number expressed in the base-2 numeral system, which uses only two digits: 0 and 1. Each binary digit represents an increasing power of 2, starting from the rightmost digit (least significant). - Octal Numbers:
Octal numbers are numbers in the base-8 numeral system, which uses digits from 0 to 7. It is commonly used in computer science as a shorthand for binary numbers, since one octal digit represents three binary digits. - Decimal Number:
Decimal numbers are numbers expressed in the base-10 numeral system, which uses digits from 0 to 9. It is the standard system for denoting integer and non-integer numbers. - Convert binary number 101012 to decimal
1×24+0×23+1×22+0×21+1×20=16+4+1=211 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 16 + 4 + 1 = 211×24+0×23+1×22+0×21+1×20=16+4+1=21
So, the decimal equivalent is 21. - Convert binary number 111112 to decimal
1×24+1×23+1×22+1×21+1×20=16+8+4+2+1=311 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 16 + 8 + 4 + 2 + 1 = 311×24+1×23+1×22+1×21+1×20=16+8+4+2+1=31
So, the decimal equivalent is 31. - Convert 110011.112 to decimal
Integer part:
1×25+1×24+0×23+0×22+1×21+1×20=32+16+2+1=511 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 32 + 16 + 2 + 1 = 511×25+1×24+0×23+0×22+1×21+1×20=32+16+2+1=51
Fractional part:
1×2−1+1×2−2=0.5+0.25=0.751 \times 2^{-1} + 1 \times 2^{-2} = 0.5 + 0.25 = 0.751×2−1+1×2−2=0.5+0.25=0.75
So, the decimal equivalent is 51.75.
