Which of the following number systems has a base of 16? Hexadecimal Binary-coded

Question

Which of the following number systems has a base of 16? Hexadecimal Binary-coded decimal Octal Gray code The number 12 is: 12 in any number system. 12 in binary. 12 in decimal. all of the above. The binary number 101 has the decimal equivalent of: 3. 41. 101. 5. The octal number 153 would be written in binary as: 011 101 001. 011 111 101. 010 100 011. 001 101 011. The octal number 62 would be written in decimal as: A12. 50. F35. 98. For a base 8 number system, the weight value associated with the third digit would be: 16. 64. 32. 512. All digital computing devices operate using the binary number system because: most people are familiar with it. large decimal numbers can be represented in a shorter

Explanation / Answer

1) Hexadecimal number system has 16 base.

2) The number 12 if we write without any base then we consider it under general number system followed which is decimal (base10) hence it will be 12 in decimal number system.

3) Binary equivalent of 101

to convert binary to decimal we start multiplying each digit with powers of 2 starting from 0(rigth to left)

1*2^2 +0* 2^1 +1*2^0
= 4+0+1
= 5

4) Octal 153 in binary

1 5 3, now write binary equivalent of eacg digit seperately

1 - 001

5 -101

3 - 011

Combine binary equivalent of each digit starting from right to obtain binary equivalent (8 bits)

= 01101011

5) Octal to decimal

Here we want to convert octal which is base 8 to decimal

We will multiply each digit with powers of 8 starting from right to left and sum up all

6 *8^1 +2*8^0
= 6*8 + 2*1
= 48+2
= 50

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