What is the denary equivalent of the hexadecimal number A7?

Let's start by looking at the denary (i.e. base 10) number system. In base 10, you have a column for each digit in a number.

For example, with the number 5,867 you have a 5 in the 1,000's column, an 8 in the 100's column, a 6 in the 10's column, and a 7 in the 1's column. Essentially, this means: (5 x 1,000) + (8 x 100) + (6 x 10) + (7 x 1), which of course comes to 5,867.

The same principle can be used for hexadecimal to denary conversion. Hexadecimal uses the base 16 number system, so instead of have a column for 1's (10⁰), 10's (10¹), 100's (10²) etc. you have a column for 16⁰, 16¹, 16² etc.

Hexadecimal uses numbers from 0-9 followed by A-F (i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F) to represent their denary equivalent 0-15. The letter A represents 10, B represents 11, and so on up to F which represents 15.

So, for the hexadecimal value A7, we have a 7 in the 16⁰ column, and an A (which as we know represents 10) in the 16¹ column. Therefore, to convert it to denary, we do:

A7 = (16¹ x 10) + (16⁰ x 7) 

= (16 x 10) + (1 x 7)

= (160) + (7)

= 167

Therefore, the hexadecimal number A7 is equal to the denary number 167.