a combinational circuit that accepts a 4-bit number and generates a 3-bit binary number output that approximates the square root of the number

Question

Design a combinational circuit that accepts a 4-bit number and generates a 3-bit binary number output that approximates the square root of the number. For example, if the square root is 3.5 or larger, give a result of 4. If the square root is < 3.5 and ≥ 2.5, give a result of 3.

Does my truth table on input goes this way? (I'm using A, B, C, D for my inputs)

    INPUTS        OUTPUTS   Decimal - Square Root Value
  __________    __________  ____________________________
  A  B  C  D    W  X  Y  Z    
  0  0  0  0    0  0  0  0     0 - 0
  0  0  0  1    0  0  0  1     1 - 1
  0  0  1  0    0  0  0  1     2 - 1.14
  0  0  1  1    0  0  1  0     3 - 1.73
  0  1  0  0    0  0  1  0     4 - 2
  0  1  0  1    0  0  1  0     5 - 2.23
  0  1  1  0    0  0  1  0     6 - 2.44
  0  1  1  1    0  0  1  1     7 - 2.64
  1  0  0  0    0  0  1  1     8 - 2.82
  1  0  0  1    0  0  1  1     9 - 3
  1  0  1  0    0  0  1  1    10 - 3.16
  1  0  1  1    0  0  1  1    11 - 3.31
  1  1  0  0    0  0  1  1    12 - 3.46
  1  1  0  1    0  1  0  0    13 - 3.60
  1  1  1  0    0  1  0  0    14 - 3.74
  1  1  1  1    0  1  0  0    15 - 3.87

I'm having trouble generating the output table with "generates a 3-bit binary number output that approximates the square root of the number" Can someone help me with the outputs? Thank you.

Answer 1

Translate your input as decimal, get square root for each of them, and translate them in binary?

Exemple: 0000 => 0 Square root of 0 is 0 0 => 0000

So you have

A|B|C|D||W|X|Y|Z

0 0 0 0||0 0 0 0

And do the rest of your homework this way?