Home/ Questions/Q 644681
In Process

The Archive Base Latest Questions

Editorial Team
  • 0
Asked: 2026-05-13T21:25:10+00:00

I understand that the first bit is the sign and that the next 8

  • 0

I understand that the first bit is the sign and that the next 8 bits is the exponent. So in this example you would have 1.1001*2^-4 ? How do I then interpret this in decimal? 

0 01111011 10010000000000000000000
Share

Leave an answer

You must login to add an answer.

Need An Account,

1 Answer

  1. Editorial Team

    Since you already figured out that this is (in binary)1.1001*10^-100, now you just have to convert the binary number to decimal.

    In decimal, each digit has a value one-tenth as much as the one before it. In binary, each digit has a value one-half as much as the one before it.

    First 1.1001*10^-100 = 0.00011001.

    Which is…

      0 * 1           0 * 1
+ 0 * 1/2       + 0 * 0.5
+ 0 * 1/4       + 0 * 0.25
+ 0 * 1/8       + 0 * 0.125
+ 1 * 1/16      + 1 * 0.0625
+ 1 * 1/32      + 1 * 0.03125
+ 0 * 1/64      + 0 * 0.015625
+ 0 * 1/128     + 0 * 0.0078125
+ 1 * 1/256     + 1 * 0.00390625

    0.0625 + 0.03125 + 0.00390625 = 0.09765625

    That’s all there is to it.

    • 0