Chapter 83, Problem 1A

To determine

To express:

A binary number into a decimal number.

Answer to Problem 1A

Decimal numbers is 52.25₁₀.

Explanation of Solution

Given information:

A binary number 110100.01₂.

Calculation:

The decimal number for integer value is equal to the summation of binary digits (d_n) multiplied by power of 2 i.e. 2ⁿ in increasing order from zero and from right to left.

The decimal number for fractional value is equal to the summation of binary digits (d_n) multiplied by negative power of 2 i.e. 2-n in increasing order from 1 and from left to right.

Decimal of any binary number is equal to

  $decimal=d_0\times 2^0+d_1\times 2^1+d_2\times 2^2+\mathrm{...}$

So decimal number of 110100.01₂ is

  $\begin{array}{l}decimal=1\times 2^5+1\times 2^4+0\times 2^3+1\times 2^2+0\times 2^1+0\times 2^0+0\times 2^{-1}+1\times 2^{-2}\\ decimal=1\times 32+1\times 16+0\times 8+1\times 4+0\times 2+0\times 1+0\times 0.5+1\times 0.25\\ decimal=32+16+0+4+0+0+0+0.25\\ decimal={52.25}_{10}\end{array}$