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 values112806413201618041201

Convert the binary number 1010 1010₂ to decimal. Find N.

1010 1010₂
N =
2.Easy
place values012816403201608041201

Convert the binary number 0100 0010₂ to decimal. Find N.

0100 0010₂
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −12 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −128 bit
U =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −13 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −138 bit
U =
5.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 0101 1111 << 3. What is the result's value R in decimal?

0101 1111<< 3
R =
6.Hard
3389 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 3389 items its own binary code of the same length. What is the smallest number of bits b needed?

3389
b = bit

Answer key

  1. 1. N = 170
  2. 2. N = 66
  3. 3. U = 244
  4. 4. U = 243
  5. 5. R = 248
  6. 6. b = 12 bit

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