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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1.Easy
place values112816403201608041201

Convert the binary number 1100 0010₂ to decimal. Find N.

1100 0010₂
N =
2.Easy
place values112816413201608141201

Convert the binary number 1110 0110₂ to decimal. Find N.

1110 0110₂
N =
3.Medium
place values in two's complement0−12816403201618040211

The 8-bit pattern 0100 1001 stores a signed integer in two's complement. What is its value N in decimal?

0100 10018 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
1916 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 1916 items its own binary code of the same length. What is the smallest number of bits b needed?

1916
b = bit
6.Hard
12 bits, unsigned, N = ?????????????

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

12 bit
N =

Answer key

  1. 1. N = 194
  2. 2. N = 230
  3. 3. N = 73
  4. 4. N = −28
  5. 5. b = 11 bit
  6. 6. N = 4095

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