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 values112806403211618141211

Convert the binary number 1001 1111₂ to decimal. Find N.

1001 1111₂
N =
2.Easy
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0xE2. What is the pattern's value N in decimal?

0xE2
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −111 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −1118 bit
U =
4.Medium
place values in two's complement1−12806413211618140211

The 8-bit pattern 1011 1101 stores a signed integer in two's complement. What is its value N in decimal?

1011 11018 bit
N =
5.Hard
3560 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 3560 items its own binary code of the same length. What is the smallest number of bits b needed?

3560
b = bit
6.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 1100 1100 OR 0011 1100. What is the result's value R in decimal?

1100 1100OR0011 1100
R =

Answer key

  1. 1. N = 159
  2. 2. N = 226
  3. 3. U = 145
  4. 4. N = −67
  5. 5. b = 12 bit
  6. 6. R = 252

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