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 values112816413201618141201

Convert the binary number 1110 1110₂ to decimal. Find N.

1110 1110₂
N =
2.Easy
place values112816403201608140201

Convert the binary number 1100 0100₂ to decimal. Find N.

1100 0100₂
N =
3.Medium
place values in two's complement0−12816413201608141211

The 8-bit pattern 0110 0111 stores a signed integer in two's complement. What is its value N in decimal?

0110 01118 bit
N =
4.Medium
8-bit two's complement0−12806403201608040201

Set the bits so they store −101 in 8-bit two's complement. Read as an unsigned number, what is the pattern's value U?

N = −1018 bit
U =
5.Hard
10-bit two's complement, N = ??sign?????????

What is the most negative integer N that can be stored in 10-bit two's complement?

10 bit
N =
6.Hard
4873 codes, b = ? bits?2ᵇ⁻¹…?4?2?1

A system must give every one of 4873 items its own binary code of the same length. What is the smallest number of bits b needed?

4873
b = bit

Answer key

  1. 1. N = 238
  2. 2. N = 196
  3. 3. N = 103
  4. 4. U = 155
  5. 5. N = −512
  6. 6. b = 13 bit

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