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
click the bits to set them012806403201608040201

Set the bits so the 8-bit register holds 0x3A. What is the pattern's value N in decimal?

0x3A
N =
2.Easy
place values112816413201608041211

Convert the binary number 1110 0011₂ to decimal. Find N.

1110 0011₂
N =
3.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −87 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −878 bit
U =
4.Medium
place values in two's complement1−12806413201608141211

The 8-bit pattern 1010 0111 stores a signed integer in two's complement. What is its value N in decimal?

1010 01118 bit
N =
5.Hard
1615 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1615 items its own binary code of the same length. What is the smallest number of bits b needed?

1615
b = bit
6.Hard
click the bits to set them012806403201608040201

Set the bits to the 8-bit result of 0111 0010 XOR 1101 1111. What is the result's value R in decimal?

0111 0010XOR1101 1111
R =

Answer key

  1. 1. N = 58
  2. 2. N = 227
  3. 3. U = 169
  4. 4. N = −89
  5. 5. b = 11 bit
  6. 6. R = 173

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