Find
a.the decimal equivalent of the octal number 7126.45
b.the decimal equivalent of the binary number 1101101.0101
c.the decimal equivalent of the hexadecimal number BAD
d.the octal equivalent of the decimal number 534
a. The decimal equivalent of the octal number 7126.45 can be found by multiplying each digit by the corresponding power of 8 and adding them up.
7 * 8^3 + 1 * 8^2 + 2 * 8^1 + 6 * 8^0 + 4 * 8^(-1) + 5 * 8^(-2)
= 3584 + 64 + 16 + 6 + 0.5 + 0.03125
= 3670.53125
So, the decimal equivalent of the octal number 7126.45 is 3670.53125.
b. The decimal equivalent of the binary number 1101101.0101 can be found by multiplying each digit by the corresponding power of 2 and adding them up.
1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 1 * 2^2 + 0 * 2^1 + 1 * 2^0 + 0 * 2^(-1) + 1 * 2^(-2) + 0 * 2^(-3) + 1 * 2^(-4)
= 64 + 32 + 0 + 8 + 4 + 0 + 1 + 0 + 0.25 + 0 + 0.0625
= 109.3125
So, the decimal equivalent of the binary number 1101101.0101 is 109.3125.
c. The decimal equivalent of the hexadecimal number BAD can be found by multiplying each digit by the corresponding power of 16 and adding them up.
11 * 16^2 + 10 * 16^1 + 13 * 16^0
= 2816 + 160 + 13
= 2989
So, the decimal equivalent of the hexadecimal number BAD is 2989.
d. The octal equivalent of the decimal number 534 can be found by repeatedly dividing the decimal number by 8 and noting down the remainders in reverse order.
534 ÷ 8 = 66 remainder 6
66 ÷ 8 = 8 remainder 2
8 ÷ 8 = 1 remainder 0
So, the octal equivalent of the decimal number 534 is 1026.