Number systems worksheet with answers

Free printable Number systems worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
place values112806403211618041201

Convert the binary number 1001 1010₂ to decimal. Find N.

1001 1010₂
N =
2.Easy
place values012816413201618140211

Convert the binary number 0110 1101₂ to decimal. Find N.

0110 1101₂
N =
3.Medium
place values in two's complement1−12806413201618140201

The 8-bit pattern 1010 1100 stores a signed integer in two's complement. What is its value N in decimal?

1010 11008 bit
N =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −81 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −818 bit
U =
5.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 1001 1111 AND 1100 0100. What is the result's value R in decimal?

1001 1111AND1100 0100
R =
6.Hard
3907 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 3907 items its own binary code of the same length. What is the smallest number of bits b needed?

3907
b = bit

Answer key

  1. 1. N = 154
  2. 2. N = 109
  3. 3. N = −84
  4. 4. U = 175
  5. 5. R = 132
  6. 6. b = 12 bit

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