1.find
a.the decimal equivalent of the octal number 7126.45
b.the decimal equivalent of the binary number 11011001.0101
c.thw decimal equivalent of the hexadecimal number BAD
d.the octal equivalent of the decimal number 534
a. To find the decimal equivalent of an octal number, we can convert each digit from octal to decimal and then sum them up.
For the octal number 7126.45, let's break it down into its individual digits:
7 x (8^3) + 1 x (8^2) + 2 x (8^1) + 6 x (8^0) + 4 x (8^-1) + 5 x (8^-2)
= 7 x 512 + 1 x 64 + 2 x 8 + 6 x 1 + 4 x 0.125 + 5 x 0.015625
= 3584 + 64 + 16 + 6 + 0.5 + 0.078125
= 3670.578125
Therefore, the decimal equivalent of the octal number 7126.45 is 3670.578125.
b. To find the decimal equivalent of a binary number, we can convert each digit from binary to decimal and then sum them up.
For the binary number 11011001.0101, let's break it down into its individual digits:
1 x (2^7) + 1 x (2^6) + 0 x (2^5) + 1 x (2^4) + 1 x (2^3) + 0 x (2^2) + 0 x (2^1) + 1 x (2^0) + 0 x (2^-1) + 1 x (2^-2) + 0 x (2^-3) + 1 x (2^-4)
= 128 + 64 + 0 + 16 + 8 + 0 + 0 + 1 + 0 + 0.25 + 0 + 0.0625
= 217.3125
Therefore, the decimal equivalent of the binary number 11011001.0101 is 217.3125.
c. To find the decimal equivalent of a hexadecimal number, we can convert each digit from hexadecimal to decimal and then sum them up.
For the hexadecimal number BAD, let's break it down into its individual digits:
11 x (16^2) + 10 x (16^1) + 13 x (16^0)
= 11 x 256 + 10 x 16 + 13 x 1
= 2816 + 160 + 13
= 2989
Therefore, the decimal equivalent of the hexadecimal number BAD is 2989.
d. To find the octal equivalent of a decimal number, we divide the decimal number by 8 and write down the remainder. Repeat this process until the quotient is 0.
For the decimal number 534, let's divide it by 8:
534 ÷ 8 = 66 remainder 6
66 ÷ 8 = 8 remainder 2
8 ÷ 8 = 1 remainder 0
1 ÷ 8 = 0 remainder 1
Reading the remainders from bottom to top, the octal equivalent of the decimal number 534 is 1026.