1.
Convert the following decimal to binary
56
Explanation
The given decimal number 56 can be converted to binary by repeatedly dividing it by 2 and noting the remainder. Starting from the right, the remainders are 0, 0, 1, 1, 1, 0, 0, 0. Reversing the remainders gives us the binary representation 00111000.
2.
Convert the folowing decimal to binary
88
Explanation
The given decimal number 88 can be converted to binary by repeatedly dividing it by 2 and noting the remainder. Starting from the rightmost digit, the remainders are 0, 0, 0, 1, 1, 0, 1, and 0. These remainders, when read from right to left, give the binary representation of 88 as 01011000.
3.
Convert the following decimal to binary
96
Explanation
The given decimal number is 96. To convert it to binary, we divide the number by 2 repeatedly and note down the remainder until the quotient becomes zero. Then, we write the remainders in reverse order to get the binary representation. In this case, the binary representation of 96 is 01100000.
4.
Convert the foowing decimal into binary
78
Explanation
The given decimal number 78 is converted into binary as 01001110.
5.
Convert the folowing binary into decimal
67
Explanation
The given binary number 01000011 represents the decimal number 67. In binary representation, each digit is a power of 2, starting from the rightmost digit. Adding up the decimal values of each digit that is 1 gives us the decimal equivalent. In this case, the decimal value of the leftmost digit (0) is 0, and the decimal value of the second leftmost digit (1) is 64. Adding them together gives us 64. The decimal value of the third leftmost digit (0) is 0, and the decimal value of the fourth leftmost digit (0) is 0. Adding them together gives us 0. Finally, the decimal value of the rightmost digit (1) is 1. Adding it to the previous sum gives us 65. Thus, the decimal equivalent of the given binary number is 67.
6.
Convert the following binary into decimal
00101000
Explanation
The given binary number is 00101000. To convert it into decimal, we need to calculate the decimal value of each bit and sum them up. The leftmost bit is the most significant bit and represents the value of 2^7 (128), while the rightmost bit represents the value of 2^0 (1). Adding up the decimal values of the set bits, we get 32 + 8 = 40. Therefore, the decimal equivalent of the given binary number is 40.
7.
Convert the following decimal to binary
56
Explanation
To convert a decimal number to binary, we divide the decimal number by 2 repeatedly and record the remainders from right to left. In this case, when we divide 56 by 2, we get a quotient of 28 and a remainder of 0. When we divide 28 by 2, we get a quotient of 14 and a remainder of 0. Continuing this process, we divide 14 by 2 to get a quotient of 7 and a remainder of 0. Finally, when we divide 7 by 2, we get a quotient of 3 and a remainder of 1. The remainders read from bottom to top give us the binary representation of 56, which is 00111000.
8.
01000110
Explanation
The given binary number "01000110" represents the decimal number 70. In binary, each digit represents a power of 2, starting from the rightmost digit. The digit "1" in the rightmost position represents 2^0, which is 1. The digit "1" in the second rightmost position represents 2^1, which is 2. The remaining digits "0" represent powers of 2 that are not present, so they are multiplied by 0. Adding up all the powers of 2, we get 64 + 4 + 2 = 70.
9.
10111110
10.
000101100100
11.
000111101001
12.
Convert the following decimal into hex
29
Explanation
The decimal number 29 can be converted to hex by dividing it by 16 repeatedly and noting the remainders. The remainders in reverse order give the hex representation. In this case, when 29 is divided by 16, the quotient is 1 and the remainder is 13. The remainder 13 corresponds to the hex digit D. Therefore, the decimal number 29 is represented as 1D in hex.
13.
Convert the decimal into hex
57
Explanation
The decimal number 57 can be converted into hexadecimal by dividing it by 16 repeatedly and noting down the remainders. The remainder of 9 corresponds to the hexadecimal digit 9. Therefore, the hexadecimal representation of 57 is 39.
14.
Convert the decimal into hex
77
Explanation
The decimal number 77 can be converted to hex by dividing it by 16 repeatedly and noting down the remainders. Starting with 77, we divide it by 16 to get a quotient of 4 and a remainder of 13. The remainder 13 corresponds to the hex digit D. The quotient 4 is less than 16, so we stop dividing. Therefore, the decimal number 77 is equal to the hex number 4D.
15.
FROM DECIMAL TO OCTAL
77
16.
Decimal to octal
99
17.
THIS PART IS TO TEST YOUR KNOWLEDGE OF VENN DIAGRAMS OR SETS
Study the following figure and answer the questions given below.
1.
How many educated people are employed ?
A.
9
B.
18
C.
20
D.
15
Explanation
In the Venn diagram, the overlapping region represents educated people who are employed. By counting the number of people in this region, we can determine the answer.
18.
How many backward people are educated ?
A.
9
B.
28
C.
14
D.
6
19.
How many backward uneducated people are employed ?
A.
14
B.
5
C.
7
D.
11
20.
How many backward people are not educated ?
A.
3
B.
14
C.
22
D.
25
Explanation
The correct answer is 22. This means that there are 22 backward people who are not educated.
21.
800 people who belong to a fitness center were asked about their exercise habits. 290 said "yes" when asked if they used the treadmill regularly, 180 said "yes" when asked if they lifted weights regularly, and 50 said "yes" to both questions. How many said "yes" to either using the treadmill regularly or lifting weights regularly?
Explanation
The question asks for the number of people who said "yes" to either using the treadmill regularly or lifting weights regularly. To find this, we can add the number of people who said "yes" to each activity and then subtract the number of people who said "yes" to both activities (to avoid counting them twice). Therefore, 290 + 180 - 50 = 420.
22.
800 people who belong to a fitness center were asked about their exercise habits. 290 said "yes" when asked if they used the treadmill regularly, 180 said "yes" when asked if they lifted weights regularly, and 50 said "yes" to both questions. How many said "yes" to using the treadmill regularly but said "no" to lifting weights regularly?