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 0xBD. What is the pattern's value N in decimal?

0xBD
N =
2.Easy
place values112806413211618041201

Convert the binary number 1011 1010₂ to decimal. Find N.

1011 1010₂
N =
3.Medium
place values in two's complement1−12806413211618041211

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

1011 10118 bit
N =
4.Medium
place values in two's complement1−12816413201608140201

The 8-bit pattern 1110 0100 stores a signed integer in two's complement. What is its value N in decimal?

1110 01008 bit
N =
5.Hard
12 bits, unsigned, N = ?????????????

What is the largest unsigned integer N that fits in 12 bits?

12 bit
N =
6.Hard
176 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 176 items its own binary code of the same length. What is the smallest number of bits b needed?

176
b = bit

Answer key

  1. 1. N = 189
  2. 2. N = 186
  3. 3. N = −69
  4. 4. N = −28
  5. 5. N = 4095
  6. 6. b = 8 bit

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