Everything Science Grade 12

14.6 CHAPTER 14. ELECTRONICS

Example 5: Conversion of Binary Numbers to Denary Numbers

QUESTION

Convert the binary number 10101 to its denaryequivalent.

SOLUTION

We start on the right. The ‘1’ on the right does indeed represent one. Thenext

‘1’ is in the third place from the right, and represents 22 = 4. The next ‘1’ is in

the fifth place from theright and represents 24 = 16. Accordingly, the binary

number 10101 represents 16+4+1 = 21 in denary notation.

Example 6: Conversion of DenaryNumbers to Binary Numbers

QUESTION

Convert the decimal number 12 to its binary equivalent.

SOLUTION

Firstly we write 12 as asum of powers of 2, so12 = 8+4. In binary,eight

is 1000, and four is 100. This means that twelve = eight + four must be

1000+100 = 1100 in binary. You could also write 12 as 1 × 8 + 1× 4 + 0×

2 + 0× 1 = 1100 in binary.

Once a number is written in binary, it can berepresented using the low and high
voltage levels of digitalelectronics. We demonstrate how this is done byshowing you
how an electronic counter works.